Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,2,Mod(16,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.16");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.g (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.598878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 31.1 | ||
Root | \(-0.309017 + 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.31 |
Dual form | 75.2.g.a.46.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.309017 | + | 0.951057i | 0.218508 | + | 0.672499i | 0.998886 | + | 0.0471903i | \(0.0150267\pi\) |
−0.780378 | + | 0.625308i | \(0.784973\pi\) | |||||||
\(3\) | −0.809017 | + | 0.587785i | −0.467086 | + | 0.339358i | ||||
\(4\) | 0.809017 | − | 0.587785i | 0.404508 | − | 0.293893i | ||||
\(5\) | 1.80902 | + | 1.31433i | 0.809017 | + | 0.587785i | ||||
\(6\) | −0.809017 | − | 0.587785i | −0.330280 | − | 0.239962i | ||||
\(7\) | −4.47214 | −1.69031 | −0.845154 | − | 0.534522i | \(-0.820491\pi\) | ||||
−0.845154 | + | 0.534522i | \(0.820491\pi\) | |||||||
\(8\) | 2.42705 | + | 1.76336i | 0.858092 | + | 0.623440i | ||||
\(9\) | 0.309017 | − | 0.951057i | 0.103006 | − | 0.317019i | ||||
\(10\) | −0.690983 | + | 2.12663i | −0.218508 | + | 0.672499i | ||||
\(11\) | −0.381966 | − | 1.17557i | −0.115167 | − | 0.354448i | 0.876815 | − | 0.480828i | \(-0.159664\pi\) |
−0.991982 | + | 0.126380i | \(0.959664\pi\) | |||||||
\(12\) | −0.309017 | + | 0.951057i | −0.0892055 | + | 0.274546i | ||||
\(13\) | 1.73607 | − | 5.34307i | 0.481499 | − | 1.48190i | −0.355490 | − | 0.934680i | \(-0.615686\pi\) |
0.836989 | − | 0.547220i | \(-0.184314\pi\) | |||||||
\(14\) | −1.38197 | − | 4.25325i | −0.369346 | − | 1.13673i | ||||
\(15\) | −2.23607 | −0.577350 | ||||||||
\(16\) | −0.309017 | + | 0.951057i | −0.0772542 | + | 0.237764i | ||||
\(17\) | −3.11803 | − | 2.26538i | −0.756234 | − | 0.549436i | 0.141519 | − | 0.989936i | \(-0.454801\pi\) |
−0.897753 | + | 0.440499i | \(0.854801\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −1.00000 | − | 0.726543i | −0.229416 | − | 0.166680i | 0.467139 | − | 0.884184i | \(-0.345285\pi\) |
−0.696555 | + | 0.717504i | \(0.745285\pi\) | |||||||
\(20\) | 2.23607 | 0.500000 | ||||||||
\(21\) | 3.61803 | − | 2.62866i | 0.789520 | − | 0.573620i | ||||
\(22\) | 1.00000 | − | 0.726543i | 0.213201 | − | 0.154899i | ||||
\(23\) | 1.38197 | + | 4.25325i | 0.288160 | + | 0.886865i | 0.985434 | + | 0.170060i | \(0.0543961\pi\) |
−0.697274 | + | 0.716805i | \(0.745604\pi\) | |||||||
\(24\) | −3.00000 | −0.612372 | ||||||||
\(25\) | 1.54508 | + | 4.75528i | 0.309017 | + | 0.951057i | ||||
\(26\) | 5.61803 | 1.10179 | ||||||||
\(27\) | 0.309017 | + | 0.951057i | 0.0594703 | + | 0.183031i | ||||
\(28\) | −3.61803 | + | 2.62866i | −0.683744 | + | 0.496769i | ||||
\(29\) | −5.35410 | + | 3.88998i | −0.994232 | + | 0.722352i | −0.960844 | − | 0.277091i | \(-0.910630\pi\) |
−0.0333880 | + | 0.999442i | \(0.510630\pi\) | |||||||
\(30\) | −0.690983 | − | 2.12663i | −0.126156 | − | 0.388267i | ||||
\(31\) | −2.23607 | − | 1.62460i | −0.401610 | − | 0.291787i | 0.368587 | − | 0.929593i | \(-0.379842\pi\) |
−0.770196 | + | 0.637807i | \(0.779842\pi\) | |||||||
\(32\) | 5.00000 | 0.883883 | ||||||||
\(33\) | 1.00000 | + | 0.726543i | 0.174078 | + | 0.126475i | ||||
\(34\) | 1.19098 | − | 3.66547i | 0.204252 | − | 0.628623i | ||||
\(35\) | −8.09017 | − | 5.87785i | −1.36749 | − | 0.993538i | ||||
\(36\) | −0.309017 | − | 0.951057i | −0.0515028 | − | 0.158509i | ||||
\(37\) | −0.954915 | + | 2.93893i | −0.156987 | + | 0.483157i | −0.998357 | − | 0.0573034i | \(-0.981750\pi\) |
0.841370 | + | 0.540460i | \(0.181750\pi\) | |||||||
\(38\) | 0.381966 | − | 1.17557i | 0.0619631 | − | 0.190703i | ||||
\(39\) | 1.73607 | + | 5.34307i | 0.277993 | + | 0.855576i | ||||
\(40\) | 2.07295 | + | 6.37988i | 0.327762 | + | 1.00875i | ||||
\(41\) | −1.11803 | + | 3.44095i | −0.174608 | + | 0.537387i | −0.999615 | − | 0.0277346i | \(-0.991171\pi\) |
0.825008 | + | 0.565121i | \(0.191171\pi\) | |||||||
\(42\) | 3.61803 | + | 2.62866i | 0.558275 | + | 0.405610i | ||||
\(43\) | 7.70820 | 1.17549 | 0.587745 | − | 0.809046i | \(-0.300016\pi\) | ||||
0.587745 | + | 0.809046i | \(0.300016\pi\) | |||||||
\(44\) | −1.00000 | − | 0.726543i | −0.150756 | − | 0.109530i | ||||
\(45\) | 1.80902 | − | 1.31433i | 0.269672 | − | 0.195928i | ||||
\(46\) | −3.61803 | + | 2.62866i | −0.533450 | + | 0.387574i | ||||
\(47\) | 0.618034 | − | 0.449028i | 0.0901495 | − | 0.0654975i | −0.541797 | − | 0.840509i | \(-0.682256\pi\) |
0.631947 | + | 0.775012i | \(0.282256\pi\) | |||||||
\(48\) | −0.309017 | − | 0.951057i | −0.0446028 | − | 0.137273i | ||||
\(49\) | 13.0000 | 1.85714 | ||||||||
\(50\) | −4.04508 | + | 2.93893i | −0.572061 | + | 0.415627i | ||||
\(51\) | 3.85410 | 0.539682 | ||||||||
\(52\) | −1.73607 | − | 5.34307i | −0.240749 | − | 0.740950i | ||||
\(53\) | −2.92705 | + | 2.12663i | −0.402061 | + | 0.292115i | −0.770380 | − | 0.637585i | \(-0.779934\pi\) |
0.368319 | + | 0.929700i | \(0.379934\pi\) | |||||||
\(54\) | −0.809017 | + | 0.587785i | −0.110093 | + | 0.0799874i | ||||
\(55\) | 0.854102 | − | 2.62866i | 0.115167 | − | 0.354448i | ||||
\(56\) | −10.8541 | − | 7.88597i | −1.45044 | − | 1.05381i | ||||
\(57\) | 1.23607 | 0.163721 | ||||||||
\(58\) | −5.35410 | − | 3.88998i | −0.703028 | − | 0.510780i | ||||
\(59\) | −1.23607 | + | 3.80423i | −0.160922 | + | 0.495268i | −0.998713 | − | 0.0507240i | \(-0.983847\pi\) |
0.837790 | + | 0.545992i | \(0.183847\pi\) | |||||||
\(60\) | −1.80902 | + | 1.31433i | −0.233543 | + | 0.169679i | ||||
\(61\) | 0.500000 | + | 1.53884i | 0.0640184 | + | 0.197028i | 0.977950 | − | 0.208840i | \(-0.0669689\pi\) |
−0.913931 | + | 0.405869i | \(0.866969\pi\) | |||||||
\(62\) | 0.854102 | − | 2.62866i | 0.108471 | − | 0.333840i | ||||
\(63\) | −1.38197 | + | 4.25325i | −0.174111 | + | 0.535860i | ||||
\(64\) | 2.16312 | + | 6.65740i | 0.270390 | + | 0.832174i | ||||
\(65\) | 10.1631 | − | 7.38394i | 1.26058 | − | 0.915865i | ||||
\(66\) | −0.381966 | + | 1.17557i | −0.0470168 | + | 0.144703i | ||||
\(67\) | −0.618034 | − | 0.449028i | −0.0755049 | − | 0.0548575i | 0.549392 | − | 0.835564i | \(-0.314859\pi\) |
−0.624897 | + | 0.780707i | \(0.714859\pi\) | |||||||
\(68\) | −3.85410 | −0.467379 | ||||||||
\(69\) | −3.61803 | − | 2.62866i | −0.435560 | − | 0.316453i | ||||
\(70\) | 3.09017 | − | 9.51057i | 0.369346 | − | 1.13673i | ||||
\(71\) | 4.23607 | − | 3.07768i | 0.502729 | − | 0.365254i | −0.307330 | − | 0.951603i | \(-0.599435\pi\) |
0.810058 | + | 0.586349i | \(0.199435\pi\) | |||||||
\(72\) | 2.42705 | − | 1.76336i | 0.286031 | − | 0.207813i | ||||
\(73\) | −2.50000 | − | 7.69421i | −0.292603 | − | 0.900539i | −0.984016 | − | 0.178080i | \(-0.943012\pi\) |
0.691413 | − | 0.722460i | \(-0.256988\pi\) | |||||||
\(74\) | −3.09017 | −0.359225 | ||||||||
\(75\) | −4.04508 | − | 2.93893i | −0.467086 | − | 0.339358i | ||||
\(76\) | −1.23607 | −0.141787 | ||||||||
\(77\) | 1.70820 | + | 5.25731i | 0.194668 | + | 0.599126i | ||||
\(78\) | −4.54508 | + | 3.30220i | −0.514630 | + | 0.373900i | ||||
\(79\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(80\) | −1.80902 | + | 1.31433i | −0.202254 | + | 0.146946i | ||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | −3.61803 | −0.399545 | ||||||||
\(83\) | −10.0902 | − | 7.33094i | −1.10754 | − | 0.804675i | −0.125266 | − | 0.992123i | \(-0.539978\pi\) |
−0.982274 | + | 0.187448i | \(0.939978\pi\) | |||||||
\(84\) | 1.38197 | − | 4.25325i | 0.150785 | − | 0.464068i | ||||
\(85\) | −2.66312 | − | 8.19624i | −0.288856 | − | 0.889007i | ||||
\(86\) | 2.38197 | + | 7.33094i | 0.256854 | + | 0.790515i | ||||
\(87\) | 2.04508 | − | 6.29412i | 0.219256 | − | 0.674801i | ||||
\(88\) | 1.14590 | − | 3.52671i | 0.122153 | − | 0.375949i | ||||
\(89\) | 1.66312 | + | 5.11855i | 0.176290 | + | 0.542566i | 0.999690 | − | 0.0248961i | \(-0.00792549\pi\) |
−0.823400 | + | 0.567462i | \(0.807925\pi\) | |||||||
\(90\) | 1.80902 | + | 1.31433i | 0.190687 | + | 0.138542i | ||||
\(91\) | −7.76393 | + | 23.8949i | −0.813881 | + | 2.50487i | ||||
\(92\) | 3.61803 | + | 2.62866i | 0.377206 | + | 0.274056i | ||||
\(93\) | 2.76393 | 0.286606 | ||||||||
\(94\) | 0.618034 | + | 0.449028i | 0.0637453 | + | 0.0463137i | ||||
\(95\) | −0.854102 | − | 2.62866i | −0.0876290 | − | 0.269694i | ||||
\(96\) | −4.04508 | + | 2.93893i | −0.412850 | + | 0.299953i | ||||
\(97\) | −1.73607 | + | 1.26133i | −0.176271 | + | 0.128068i | −0.672422 | − | 0.740168i | \(-0.734746\pi\) |
0.496151 | + | 0.868236i | \(0.334746\pi\) | |||||||
\(98\) | 4.01722 | + | 12.3637i | 0.405801 | + | 1.24893i | ||||
\(99\) | −1.23607 | −0.124230 | ||||||||
\(100\) | 4.04508 | + | 2.93893i | 0.404508 | + | 0.293893i | ||||
\(101\) | 3.56231 | 0.354463 | 0.177231 | − | 0.984169i | \(-0.443286\pi\) | ||||
0.177231 | + | 0.984169i | \(0.443286\pi\) | |||||||
\(102\) | 1.19098 | + | 3.66547i | 0.117925 | + | 0.362935i | ||||
\(103\) | −2.61803 | + | 1.90211i | −0.257963 | + | 0.187421i | −0.709248 | − | 0.704959i | \(-0.750966\pi\) |
0.451286 | + | 0.892379i | \(0.350966\pi\) | |||||||
\(104\) | 13.6353 | − | 9.90659i | 1.33705 | − | 0.971421i | ||||
\(105\) | 10.0000 | 0.975900 | ||||||||
\(106\) | −2.92705 | − | 2.12663i | −0.284300 | − | 0.206556i | ||||
\(107\) | 7.52786 | 0.727746 | 0.363873 | − | 0.931449i | \(-0.381454\pi\) | ||||
0.363873 | + | 0.931449i | \(0.381454\pi\) | |||||||
\(108\) | 0.809017 | + | 0.587785i | 0.0778477 | + | 0.0565597i | ||||
\(109\) | −2.44427 | + | 7.52270i | −0.234119 | + | 0.720544i | 0.763118 | + | 0.646259i | \(0.223667\pi\) |
−0.997237 | + | 0.0742847i | \(0.976333\pi\) | |||||||
\(110\) | 2.76393 | 0.263531 | ||||||||
\(111\) | −0.954915 | − | 2.93893i | −0.0906365 | − | 0.278951i | ||||
\(112\) | 1.38197 | − | 4.25325i | 0.130584 | − | 0.401895i | ||||
\(113\) | 5.66312 | − | 17.4293i | 0.532741 | − | 1.63961i | −0.215738 | − | 0.976451i | \(-0.569216\pi\) |
0.748479 | − | 0.663158i | \(-0.230784\pi\) | |||||||
\(114\) | 0.381966 | + | 1.17557i | 0.0357744 | + | 0.110102i | ||||
\(115\) | −3.09017 | + | 9.51057i | −0.288160 | + | 0.886865i | ||||
\(116\) | −2.04508 | + | 6.29412i | −0.189881 | + | 0.584395i | ||||
\(117\) | −4.54508 | − | 3.30220i | −0.420193 | − | 0.305288i | ||||
\(118\) | −4.00000 | −0.368230 | ||||||||
\(119\) | 13.9443 | + | 10.1311i | 1.27827 | + | 0.928717i | ||||
\(120\) | −5.42705 | − | 3.94298i | −0.495420 | − | 0.359943i | ||||
\(121\) | 7.66312 | − | 5.56758i | 0.696647 | − | 0.506144i | ||||
\(122\) | −1.30902 | + | 0.951057i | −0.118513 | + | 0.0861046i | ||||
\(123\) | −1.11803 | − | 3.44095i | −0.100810 | − | 0.310260i | ||||
\(124\) | −2.76393 | −0.248208 | ||||||||
\(125\) | −3.45492 | + | 10.6331i | −0.309017 | + | 0.951057i | ||||
\(126\) | −4.47214 | −0.398410 | ||||||||
\(127\) | −1.14590 | − | 3.52671i | −0.101682 | − | 0.312945i | 0.887255 | − | 0.461279i | \(-0.152609\pi\) |
−0.988937 | + | 0.148333i | \(0.952609\pi\) | |||||||
\(128\) | 2.42705 | − | 1.76336i | 0.214523 | − | 0.155860i | ||||
\(129\) | −6.23607 | + | 4.53077i | −0.549055 | + | 0.398912i | ||||
\(130\) | 10.1631 | + | 7.38394i | 0.891364 | + | 0.647614i | ||||
\(131\) | 6.61803 | + | 4.80828i | 0.578220 | + | 0.420102i | 0.838082 | − | 0.545544i | \(-0.183677\pi\) |
−0.259862 | + | 0.965646i | \(0.583677\pi\) | |||||||
\(132\) | 1.23607 | 0.107586 | ||||||||
\(133\) | 4.47214 | + | 3.24920i | 0.387783 | + | 0.281741i | ||||
\(134\) | 0.236068 | − | 0.726543i | 0.0203932 | − | 0.0627637i | ||||
\(135\) | −0.690983 | + | 2.12663i | −0.0594703 | + | 0.183031i | ||||
\(136\) | −3.57295 | − | 10.9964i | −0.306378 | − | 0.942934i | ||||
\(137\) | −2.35410 | + | 7.24518i | −0.201125 | + | 0.618998i | 0.798726 | + | 0.601695i | \(0.205508\pi\) |
−0.999850 | + | 0.0173024i | \(0.994492\pi\) | |||||||
\(138\) | 1.38197 | − | 4.25325i | 0.117641 | − | 0.362061i | ||||
\(139\) | −7.09017 | − | 21.8213i | −0.601380 | − | 1.85086i | −0.519983 | − | 0.854177i | \(-0.674062\pi\) |
−0.0813976 | − | 0.996682i | \(-0.525938\pi\) | |||||||
\(140\) | −10.0000 | −0.845154 | ||||||||
\(141\) | −0.236068 | + | 0.726543i | −0.0198805 | + | 0.0611859i | ||||
\(142\) | 4.23607 | + | 3.07768i | 0.355483 | + | 0.258273i | ||||
\(143\) | −6.94427 | −0.580709 | ||||||||
\(144\) | 0.809017 | + | 0.587785i | 0.0674181 | + | 0.0489821i | ||||
\(145\) | −14.7984 | −1.22894 | ||||||||
\(146\) | 6.54508 | − | 4.75528i | 0.541675 | − | 0.393550i | ||||
\(147\) | −10.5172 | + | 7.64121i | −0.867446 | + | 0.630236i | ||||
\(148\) | 0.954915 | + | 2.93893i | 0.0784935 | + | 0.241578i | ||||
\(149\) | −18.8541 | −1.54459 | −0.772294 | − | 0.635265i | \(-0.780891\pi\) | ||||
−0.772294 | + | 0.635265i | \(0.780891\pi\) | |||||||
\(150\) | 1.54508 | − | 4.75528i | 0.126156 | − | 0.388267i | ||||
\(151\) | 7.52786 | 0.612609 | 0.306304 | − | 0.951934i | \(-0.400907\pi\) | ||||
0.306304 | + | 0.951934i | \(0.400907\pi\) | |||||||
\(152\) | −1.14590 | − | 3.52671i | −0.0929446 | − | 0.286054i | ||||
\(153\) | −3.11803 | + | 2.26538i | −0.252078 | + | 0.183145i | ||||
\(154\) | −4.47214 | + | 3.24920i | −0.360375 | + | 0.261828i | ||||
\(155\) | −1.90983 | − | 5.87785i | −0.153401 | − | 0.472120i | ||||
\(156\) | 4.54508 | + | 3.30220i | 0.363898 | + | 0.264387i | ||||
\(157\) | 10.7984 | 0.861804 | 0.430902 | − | 0.902399i | \(-0.358195\pi\) | ||||
0.430902 | + | 0.902399i | \(0.358195\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.11803 | − | 3.44095i | 0.0886659 | − | 0.272885i | ||||
\(160\) | 9.04508 | + | 6.57164i | 0.715077 | + | 0.519534i | ||||
\(161\) | −6.18034 | − | 19.0211i | −0.487079 | − | 1.49908i | ||||
\(162\) | 0.309017 | − | 0.951057i | 0.0242787 | − | 0.0747221i | ||||
\(163\) | −4.61803 | + | 14.2128i | −0.361712 | + | 1.11324i | 0.590302 | + | 0.807183i | \(0.299009\pi\) |
−0.952014 | + | 0.306054i | \(0.900991\pi\) | |||||||
\(164\) | 1.11803 | + | 3.44095i | 0.0873038 | + | 0.268693i | ||||
\(165\) | 0.854102 | + | 2.62866i | 0.0664917 | + | 0.204641i | ||||
\(166\) | 3.85410 | − | 11.8617i | 0.299136 | − | 0.920647i | ||||
\(167\) | −2.76393 | − | 2.00811i | −0.213879 | − | 0.155393i | 0.475688 | − | 0.879614i | \(-0.342199\pi\) |
−0.689567 | + | 0.724222i | \(0.742199\pi\) | |||||||
\(168\) | 13.4164 | 1.03510 | ||||||||
\(169\) | −15.0172 | − | 10.9106i | −1.15517 | − | 0.839281i | ||||
\(170\) | 6.97214 | − | 5.06555i | 0.534738 | − | 0.388510i | ||||
\(171\) | −1.00000 | + | 0.726543i | −0.0764719 | + | 0.0555601i | ||||
\(172\) | 6.23607 | − | 4.53077i | 0.475496 | − | 0.345468i | ||||
\(173\) | 6.51722 | + | 20.0579i | 0.495495 | + | 1.52498i | 0.816184 | + | 0.577793i | \(0.196086\pi\) |
−0.320689 | + | 0.947185i | \(0.603914\pi\) | |||||||
\(174\) | 6.61803 | 0.501712 | ||||||||
\(175\) | −6.90983 | − | 21.2663i | −0.522334 | − | 1.60758i | ||||
\(176\) | 1.23607 | 0.0931721 | ||||||||
\(177\) | −1.23607 | − | 3.80423i | −0.0929086 | − | 0.285943i | ||||
\(178\) | −4.35410 | + | 3.16344i | −0.326354 | + | 0.237110i | ||||
\(179\) | 13.0902 | − | 9.51057i | 0.978405 | − | 0.710853i | 0.0210536 | − | 0.999778i | \(-0.493298\pi\) |
0.957352 | + | 0.288925i | \(0.0932979\pi\) | |||||||
\(180\) | 0.690983 | − | 2.12663i | 0.0515028 | − | 0.158509i | ||||
\(181\) | −11.9721 | − | 8.69827i | −0.889882 | − | 0.646537i | 0.0459654 | − | 0.998943i | \(-0.485364\pi\) |
−0.935847 | + | 0.352406i | \(0.885364\pi\) | |||||||
\(182\) | −25.1246 | −1.86236 | ||||||||
\(183\) | −1.30902 | − | 0.951057i | −0.0967653 | − | 0.0703041i | ||||
\(184\) | −4.14590 | + | 12.7598i | −0.305640 | + | 0.940662i | ||||
\(185\) | −5.59017 | + | 4.06150i | −0.410997 | + | 0.298607i | ||||
\(186\) | 0.854102 | + | 2.62866i | 0.0626258 | + | 0.192742i | ||||
\(187\) | −1.47214 | + | 4.53077i | −0.107653 | + | 0.331323i | ||||
\(188\) | 0.236068 | − | 0.726543i | 0.0172170 | − | 0.0529886i | ||||
\(189\) | −1.38197 | − | 4.25325i | −0.100523 | − | 0.309379i | ||||
\(190\) | 2.23607 | − | 1.62460i | 0.162221 | − | 0.117861i | ||||
\(191\) | 2.05573 | − | 6.32688i | 0.148747 | − | 0.457797i | −0.848727 | − | 0.528832i | \(-0.822630\pi\) |
0.997474 | + | 0.0710349i | \(0.0226302\pi\) | |||||||
\(192\) | −5.66312 | − | 4.11450i | −0.408700 | − | 0.296938i | ||||
\(193\) | 23.3262 | 1.67906 | 0.839530 | − | 0.543314i | \(-0.182831\pi\) | ||||
0.839530 | + | 0.543314i | \(0.182831\pi\) | |||||||
\(194\) | −1.73607 | − | 1.26133i | −0.124642 | − | 0.0905580i | ||||
\(195\) | −3.88197 | + | 11.9475i | −0.277993 | + | 0.855576i | ||||
\(196\) | 10.5172 | − | 7.64121i | 0.751230 | − | 0.545801i | ||||
\(197\) | −6.16312 | + | 4.47777i | −0.439104 | + | 0.319028i | −0.785279 | − | 0.619142i | \(-0.787480\pi\) |
0.346175 | + | 0.938170i | \(0.387480\pi\) | |||||||
\(198\) | −0.381966 | − | 1.17557i | −0.0271451 | − | 0.0835442i | ||||
\(199\) | 12.6525 | 0.896910 | 0.448455 | − | 0.893805i | \(-0.351974\pi\) | ||||
0.448455 | + | 0.893805i | \(0.351974\pi\) | |||||||
\(200\) | −4.63525 | + | 14.2658i | −0.327762 | + | 1.00875i | ||||
\(201\) | 0.763932 | 0.0538836 | ||||||||
\(202\) | 1.10081 | + | 3.38795i | 0.0774529 | + | 0.238376i | ||||
\(203\) | 23.9443 | − | 17.3965i | 1.68056 | − | 1.22100i | ||||
\(204\) | 3.11803 | − | 2.26538i | 0.218306 | − | 0.158609i | ||||
\(205\) | −6.54508 | + | 4.75528i | −0.457129 | + | 0.332123i | ||||
\(206\) | −2.61803 | − | 1.90211i | −0.182407 | − | 0.132526i | ||||
\(207\) | 4.47214 | 0.310835 | ||||||||
\(208\) | 4.54508 | + | 3.30220i | 0.315145 | + | 0.228966i | ||||
\(209\) | −0.472136 | + | 1.45309i | −0.0326583 | + | 0.100512i | ||||
\(210\) | 3.09017 | + | 9.51057i | 0.213242 | + | 0.656291i | ||||
\(211\) | 5.52786 | + | 17.0130i | 0.380554 | + | 1.17122i | 0.939655 | + | 0.342125i | \(0.111146\pi\) |
−0.559101 | + | 0.829100i | \(0.688854\pi\) | |||||||
\(212\) | −1.11803 | + | 3.44095i | −0.0767869 | + | 0.236326i | ||||
\(213\) | −1.61803 | + | 4.97980i | −0.110866 | + | 0.341210i | ||||
\(214\) | 2.32624 | + | 7.15942i | 0.159018 | + | 0.489408i | ||||
\(215\) | 13.9443 | + | 10.1311i | 0.950991 | + | 0.690936i | ||||
\(216\) | −0.927051 | + | 2.85317i | −0.0630778 | + | 0.194134i | ||||
\(217\) | 10.0000 | + | 7.26543i | 0.678844 | + | 0.493209i | ||||
\(218\) | −7.90983 | −0.535721 | ||||||||
\(219\) | 6.54508 | + | 4.75528i | 0.442276 | + | 0.321332i | ||||
\(220\) | −0.854102 | − | 2.62866i | −0.0575835 | − | 0.177224i | ||||
\(221\) | −17.5172 | + | 12.7270i | −1.17834 | + | 0.856111i | ||||
\(222\) | 2.50000 | − | 1.81636i | 0.167789 | − | 0.121906i | ||||
\(223\) | 2.52786 | + | 7.77997i | 0.169278 | + | 0.520985i | 0.999326 | − | 0.0367073i | \(-0.0116869\pi\) |
−0.830048 | + | 0.557692i | \(0.811687\pi\) | |||||||
\(224\) | −22.3607 | −1.49404 | ||||||||
\(225\) | 5.00000 | 0.333333 | ||||||||
\(226\) | 18.3262 | 1.21904 | ||||||||
\(227\) | −6.18034 | − | 19.0211i | −0.410204 | − | 1.26248i | −0.916471 | − | 0.400100i | \(-0.868975\pi\) |
0.506268 | − | 0.862376i | \(-0.331025\pi\) | |||||||
\(228\) | 1.00000 | − | 0.726543i | 0.0662266 | − | 0.0481165i | ||||
\(229\) | −17.7812 | + | 12.9188i | −1.17501 | + | 0.853696i | −0.991600 | − | 0.129340i | \(-0.958714\pi\) |
−0.183411 | + | 0.983036i | \(0.558714\pi\) | |||||||
\(230\) | −10.0000 | −0.659380 | ||||||||
\(231\) | −4.47214 | − | 3.24920i | −0.294245 | − | 0.213781i | ||||
\(232\) | −19.8541 | −1.30349 | ||||||||
\(233\) | −10.0172 | − | 7.27794i | −0.656250 | − | 0.476794i | 0.209144 | − | 0.977885i | \(-0.432932\pi\) |
−0.865394 | + | 0.501091i | \(0.832932\pi\) | |||||||
\(234\) | 1.73607 | − | 5.34307i | 0.113490 | − | 0.349287i | ||||
\(235\) | 1.70820 | 0.111431 | ||||||||
\(236\) | 1.23607 | + | 3.80423i | 0.0804612 | + | 0.247634i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.32624 | + | 16.3925i | −0.345249 | + | 1.06257i | ||||
\(239\) | −7.70820 | − | 23.7234i | −0.498602 | − | 1.53454i | −0.811267 | − | 0.584676i | \(-0.801222\pi\) |
0.312664 | − | 0.949864i | \(-0.398778\pi\) | |||||||
\(240\) | 0.690983 | − | 2.12663i | 0.0446028 | − | 0.137273i | ||||
\(241\) | 8.66312 | − | 26.6623i | 0.558041 | − | 1.71747i | −0.129735 | − | 0.991549i | \(-0.541413\pi\) |
0.687775 | − | 0.725923i | \(-0.258587\pi\) | |||||||
\(242\) | 7.66312 | + | 5.56758i | 0.492604 | + | 0.357898i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 1.30902 | + | 0.951057i | 0.0838012 | + | 0.0608852i | ||||
\(245\) | 23.5172 | + | 17.0863i | 1.50246 | + | 1.09160i | ||||
\(246\) | 2.92705 | − | 2.12663i | 0.186622 | − | 0.135589i | ||||
\(247\) | −5.61803 | + | 4.08174i | −0.357467 | + | 0.259715i | ||||
\(248\) | −2.56231 | − | 7.88597i | −0.162707 | − | 0.500759i | ||||
\(249\) | 12.4721 | 0.790390 | ||||||||
\(250\) | −11.1803 | −0.707107 | ||||||||
\(251\) | −9.05573 | −0.571592 | −0.285796 | − | 0.958290i | \(-0.592258\pi\) | ||||
−0.285796 | + | 0.958290i | \(0.592258\pi\) | |||||||
\(252\) | 1.38197 | + | 4.25325i | 0.0870557 | + | 0.267930i | ||||
\(253\) | 4.47214 | − | 3.24920i | 0.281161 | − | 0.204275i | ||||
\(254\) | 3.00000 | − | 2.17963i | 0.188237 | − | 0.136762i | ||||
\(255\) | 6.97214 | + | 5.06555i | 0.436612 | + | 0.317217i | ||||
\(256\) | 13.7533 | + | 9.99235i | 0.859581 | + | 0.624522i | ||||
\(257\) | 11.7984 | 0.735962 | 0.367981 | − | 0.929833i | \(-0.380049\pi\) | ||||
0.367981 | + | 0.929833i | \(0.380049\pi\) | |||||||
\(258\) | −6.23607 | − | 4.53077i | −0.388241 | − | 0.282073i | ||||
\(259\) | 4.27051 | − | 13.1433i | 0.265357 | − | 0.816684i | ||||
\(260\) | 3.88197 | − | 11.9475i | 0.240749 | − | 0.740950i | ||||
\(261\) | 2.04508 | + | 6.29412i | 0.126588 | + | 0.389597i | ||||
\(262\) | −2.52786 | + | 7.77997i | −0.156172 | + | 0.480648i | ||||
\(263\) | −7.38197 | + | 22.7194i | −0.455192 | + | 1.40094i | 0.415719 | + | 0.909493i | \(0.363530\pi\) |
−0.870910 | + | 0.491442i | \(0.836470\pi\) | |||||||
\(264\) | 1.14590 | + | 3.52671i | 0.0705251 | + | 0.217054i | ||||
\(265\) | −8.09017 | −0.496975 | ||||||||
\(266\) | −1.70820 | + | 5.25731i | −0.104737 | + | 0.322346i | ||||
\(267\) | −4.35410 | − | 3.16344i | −0.266467 | − | 0.193599i | ||||
\(268\) | −0.763932 | −0.0466646 | ||||||||
\(269\) | 5.54508 | + | 4.02874i | 0.338090 | + | 0.245637i | 0.743855 | − | 0.668341i | \(-0.232995\pi\) |
−0.405766 | + | 0.913977i | \(0.632995\pi\) | |||||||
\(270\) | −2.23607 | −0.136083 | ||||||||
\(271\) | 0.145898 | − | 0.106001i | 0.00886267 | − | 0.00643911i | −0.583345 | − | 0.812224i | \(-0.698256\pi\) |
0.592208 | + | 0.805785i | \(0.298256\pi\) | |||||||
\(272\) | 3.11803 | − | 2.26538i | 0.189059 | − | 0.137359i | ||||
\(273\) | −7.76393 | − | 23.8949i | −0.469895 | − | 1.44619i | ||||
\(274\) | −7.61803 | −0.460222 | ||||||||
\(275\) | 5.00000 | − | 3.63271i | 0.301511 | − | 0.219061i | ||||
\(276\) | −4.47214 | −0.269191 | ||||||||
\(277\) | 5.80902 | + | 17.8783i | 0.349030 | + | 1.07420i | 0.959391 | + | 0.282080i | \(0.0910245\pi\) |
−0.610361 | + | 0.792124i | \(0.708976\pi\) | |||||||
\(278\) | 18.5623 | − | 13.4863i | 1.11329 | − | 0.808855i | ||||
\(279\) | −2.23607 | + | 1.62460i | −0.133870 | + | 0.0972622i | ||||
\(280\) | −9.27051 | − | 28.5317i | −0.554019 | − | 1.70509i | ||||
\(281\) | 15.8713 | + | 11.5312i | 0.946804 | + | 0.687893i | 0.950049 | − | 0.312102i | \(-0.101033\pi\) |
−0.00324500 | + | 0.999995i | \(0.501033\pi\) | |||||||
\(282\) | −0.763932 | −0.0454915 | ||||||||
\(283\) | −11.0902 | − | 8.05748i | −0.659242 | − | 0.478967i | 0.207165 | − | 0.978306i | \(-0.433576\pi\) |
−0.866407 | + | 0.499339i | \(0.833576\pi\) | |||||||
\(284\) | 1.61803 | − | 4.97980i | 0.0960127 | − | 0.295497i | ||||
\(285\) | 2.23607 | + | 1.62460i | 0.132453 | + | 0.0962329i | ||||
\(286\) | −2.14590 | − | 6.60440i | −0.126890 | − | 0.390526i | ||||
\(287\) | 5.00000 | − | 15.3884i | 0.295141 | − | 0.908350i | ||||
\(288\) | 1.54508 | − | 4.75528i | 0.0910450 | − | 0.280208i | ||||
\(289\) | −0.663119 | − | 2.04087i | −0.0390070 | − | 0.120051i | ||||
\(290\) | −4.57295 | − | 14.0741i | −0.268533 | − | 0.826459i | ||||
\(291\) | 0.663119 | − | 2.04087i | 0.0388727 | − | 0.119638i | ||||
\(292\) | −6.54508 | − | 4.75528i | −0.383022 | − | 0.278282i | ||||
\(293\) | −20.7984 | −1.21505 | −0.607527 | − | 0.794299i | \(-0.707838\pi\) | ||||
−0.607527 | + | 0.794299i | \(0.707838\pi\) | |||||||
\(294\) | −10.5172 | − | 7.64121i | −0.613377 | − | 0.445644i | ||||
\(295\) | −7.23607 | + | 5.25731i | −0.421300 | + | 0.306092i | ||||
\(296\) | −7.50000 | + | 5.44907i | −0.435929 | + | 0.316721i | ||||
\(297\) | 1.00000 | − | 0.726543i | 0.0580259 | − | 0.0421583i | ||||
\(298\) | −5.82624 | − | 17.9313i | −0.337505 | − | 1.03873i | ||||
\(299\) | 25.1246 | 1.45299 | ||||||||
\(300\) | −5.00000 | −0.288675 | ||||||||
\(301\) | −34.4721 | −1.98694 | ||||||||
\(302\) | 2.32624 | + | 7.15942i | 0.133860 | + | 0.411979i | ||||
\(303\) | −2.88197 | + | 2.09387i | −0.165565 | + | 0.120290i | ||||
\(304\) | 1.00000 | − | 0.726543i | 0.0573539 | − | 0.0416701i | ||||
\(305\) | −1.11803 | + | 3.44095i | −0.0640184 | + | 0.197028i | ||||
\(306\) | −3.11803 | − | 2.26538i | −0.178246 | − | 0.129503i | ||||
\(307\) | 32.6525 | 1.86358 | 0.931788 | − | 0.363004i | \(-0.118249\pi\) | ||||
0.931788 | + | 0.363004i | \(0.118249\pi\) | |||||||
\(308\) | 4.47214 | + | 3.24920i | 0.254824 | + | 0.185140i | ||||
\(309\) | 1.00000 | − | 3.07768i | 0.0568880 | − | 0.175083i | ||||
\(310\) | 5.00000 | − | 3.63271i | 0.283981 | − | 0.206324i | ||||
\(311\) | 5.47214 | + | 16.8415i | 0.310296 | + | 0.954994i | 0.977647 | + | 0.210251i | \(0.0674280\pi\) |
−0.667351 | + | 0.744743i | \(0.732572\pi\) | |||||||
\(312\) | −5.20820 | + | 16.0292i | −0.294856 | + | 0.907475i | ||||
\(313\) | −0.145898 | + | 0.449028i | −0.00824664 | + | 0.0253806i | −0.955095 | − | 0.296299i | \(-0.904247\pi\) |
0.946849 | + | 0.321680i | \(0.104247\pi\) | |||||||
\(314\) | 3.33688 | + | 10.2699i | 0.188311 | + | 0.579562i | ||||
\(315\) | −8.09017 | + | 5.87785i | −0.455829 | + | 0.331179i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −23.3262 | − | 16.9475i | −1.31013 | − | 0.951867i | −0.999999 | − | 0.00117338i | \(-0.999627\pi\) |
−0.310133 | − | 0.950693i | \(-0.600373\pi\) | |||||||
\(318\) | 3.61803 | 0.202889 | ||||||||
\(319\) | 6.61803 | + | 4.80828i | 0.370539 | + | 0.269212i | ||||
\(320\) | −4.83688 | + | 14.8864i | −0.270390 | + | 0.832174i | ||||
\(321\) | −6.09017 | + | 4.42477i | −0.339920 | + | 0.246966i | ||||
\(322\) | 16.1803 | − | 11.7557i | 0.901695 | − | 0.655120i | ||||
\(323\) | 1.47214 | + | 4.53077i | 0.0819118 | + | 0.252099i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 28.0902 | 1.55816 | ||||||||
\(326\) | −14.9443 | −0.827687 | ||||||||
\(327\) | −2.44427 | − | 7.52270i | −0.135169 | − | 0.416006i | ||||
\(328\) | −8.78115 | + | 6.37988i | −0.484858 | + | 0.352270i | ||||
\(329\) | −2.76393 | + | 2.00811i | −0.152381 | + | 0.110711i | ||||
\(330\) | −2.23607 | + | 1.62460i | −0.123091 | + | 0.0894312i | ||||
\(331\) | 5.61803 | + | 4.08174i | 0.308795 | + | 0.224353i | 0.731379 | − | 0.681971i | \(-0.238877\pi\) |
−0.422584 | + | 0.906324i | \(0.638877\pi\) | |||||||
\(332\) | −12.4721 | −0.684497 | ||||||||
\(333\) | 2.50000 | + | 1.81636i | 0.136999 | + | 0.0995357i | ||||
\(334\) | 1.05573 | − | 3.24920i | 0.0577669 | − | 0.177788i | ||||
\(335\) | −0.527864 | − | 1.62460i | −0.0288403 | − | 0.0887613i | ||||
\(336\) | 1.38197 | + | 4.25325i | 0.0753924 | + | 0.232034i | ||||
\(337\) | 0.909830 | − | 2.80017i | 0.0495616 | − | 0.152535i | −0.923213 | − | 0.384289i | \(-0.874447\pi\) |
0.972774 | + | 0.231754i | \(0.0744465\pi\) | |||||||
\(338\) | 5.73607 | − | 17.6538i | 0.312001 | − | 0.960240i | ||||
\(339\) | 5.66312 | + | 17.4293i | 0.307578 | + | 0.946629i | ||||
\(340\) | −6.97214 | − | 5.06555i | −0.378117 | − | 0.274718i | ||||
\(341\) | −1.05573 | + | 3.24920i | −0.0571709 | + | 0.175954i | ||||
\(342\) | −1.00000 | − | 0.726543i | −0.0540738 | − | 0.0392869i | ||||
\(343\) | −26.8328 | −1.44884 | ||||||||
\(344\) | 18.7082 | + | 13.5923i | 1.00868 | + | 0.732848i | ||||
\(345\) | −3.09017 | − | 9.51057i | −0.166369 | − | 0.512032i | ||||
\(346\) | −17.0623 | + | 12.3965i | −0.917275 | + | 0.666439i | ||||
\(347\) | 16.4164 | − | 11.9272i | 0.881279 | − | 0.640287i | −0.0523106 | − | 0.998631i | \(-0.516659\pi\) |
0.933590 | + | 0.358344i | \(0.116659\pi\) | |||||||
\(348\) | −2.04508 | − | 6.29412i | −0.109628 | − | 0.337400i | ||||
\(349\) | −4.03444 | −0.215959 | −0.107979 | − | 0.994153i | \(-0.534438\pi\) | ||||
−0.107979 | + | 0.994153i | \(0.534438\pi\) | |||||||
\(350\) | 18.0902 | − | 13.1433i | 0.966960 | − | 0.702538i | ||||
\(351\) | 5.61803 | 0.299868 | ||||||||
\(352\) | −1.90983 | − | 5.87785i | −0.101794 | − | 0.313291i | ||||
\(353\) | −11.6180 | + | 8.44100i | −0.618366 | + | 0.449269i | −0.852350 | − | 0.522971i | \(-0.824823\pi\) |
0.233985 | + | 0.972240i | \(0.424823\pi\) | |||||||
\(354\) | 3.23607 | − | 2.35114i | 0.171995 | − | 0.124962i | ||||
\(355\) | 11.7082 | 0.621407 | ||||||||
\(356\) | 4.35410 | + | 3.16344i | 0.230767 | + | 0.167662i | ||||
\(357\) | −17.2361 | −0.912229 | ||||||||
\(358\) | 13.0902 | + | 9.51057i | 0.691837 | + | 0.502649i | ||||
\(359\) | −11.5623 | + | 35.5851i | −0.610235 | + | 1.87811i | −0.154507 | + | 0.987992i | \(0.549379\pi\) |
−0.455728 | + | 0.890119i | \(0.650621\pi\) | |||||||
\(360\) | 6.70820 | 0.353553 | ||||||||
\(361\) | −5.39919 | − | 16.6170i | −0.284168 | − | 0.874578i | ||||
\(362\) | 4.57295 | − | 14.0741i | 0.240349 | − | 0.739718i | ||||
\(363\) | −2.92705 | + | 9.00854i | −0.153630 | + | 0.472826i | ||||
\(364\) | 7.76393 | + | 23.8949i | 0.406941 | + | 1.25243i | ||||
\(365\) | 5.59017 | − | 17.2048i | 0.292603 | − | 0.900539i | ||||
\(366\) | 0.500000 | − | 1.53884i | 0.0261354 | − | 0.0804365i | ||||
\(367\) | 4.85410 | + | 3.52671i | 0.253382 | + | 0.184093i | 0.707224 | − | 0.706989i | \(-0.249947\pi\) |
−0.453842 | + | 0.891082i | \(0.649947\pi\) | |||||||
\(368\) | −4.47214 | −0.233126 | ||||||||
\(369\) | 2.92705 | + | 2.12663i | 0.152376 | + | 0.110708i | ||||
\(370\) | −5.59017 | − | 4.06150i | −0.290619 | − | 0.211147i | ||||
\(371\) | 13.0902 | − | 9.51057i | 0.679608 | − | 0.493764i | ||||
\(372\) | 2.23607 | − | 1.62460i | 0.115935 | − | 0.0842315i | ||||
\(373\) | 0.798374 | + | 2.45714i | 0.0413382 | + | 0.127226i | 0.969596 | − | 0.244712i | \(-0.0786934\pi\) |
−0.928258 | + | 0.371938i | \(0.878693\pi\) | |||||||
\(374\) | −4.76393 | −0.246337 | ||||||||
\(375\) | −3.45492 | − | 10.6331i | −0.178411 | − | 0.549093i | ||||
\(376\) | 2.29180 | 0.118190 | ||||||||
\(377\) | 11.4894 | + | 35.3606i | 0.591732 | + | 1.82116i | ||||
\(378\) | 3.61803 | − | 2.62866i | 0.186092 | − | 0.135203i | ||||
\(379\) | 2.76393 | − | 2.00811i | 0.141974 | − | 0.103150i | −0.514531 | − | 0.857472i | \(-0.672034\pi\) |
0.656505 | + | 0.754322i | \(0.272034\pi\) | |||||||
\(380\) | −2.23607 | − | 1.62460i | −0.114708 | − | 0.0833401i | ||||
\(381\) | 3.00000 | + | 2.17963i | 0.153695 | + | 0.111666i | ||||
\(382\) | 6.65248 | 0.340370 | ||||||||
\(383\) | 26.5623 | + | 19.2986i | 1.35727 | + | 0.986115i | 0.998613 | + | 0.0526453i | \(0.0167653\pi\) |
0.358657 | + | 0.933469i | \(0.383235\pi\) | |||||||
\(384\) | −0.927051 | + | 2.85317i | −0.0473084 | + | 0.145600i | ||||
\(385\) | −3.81966 | + | 11.7557i | −0.194668 | + | 0.599126i | ||||
\(386\) | 7.20820 | + | 22.1846i | 0.366888 | + | 1.12916i | ||||
\(387\) | 2.38197 | − | 7.33094i | 0.121082 | − | 0.372652i | ||||
\(388\) | −0.663119 | + | 2.04087i | −0.0336648 | + | 0.103609i | ||||
\(389\) | −8.00658 | − | 24.6417i | −0.405950 | − | 1.24938i | −0.920100 | − | 0.391684i | \(-0.871893\pi\) |
0.514150 | − | 0.857700i | \(-0.328107\pi\) | |||||||
\(390\) | −12.5623 | −0.636117 | ||||||||
\(391\) | 5.32624 | − | 16.3925i | 0.269359 | − | 0.829003i | ||||
\(392\) | 31.5517 | + | 22.9236i | 1.59360 | + | 1.15782i | ||||
\(393\) | −8.18034 | −0.412644 | ||||||||
\(394\) | −6.16312 | − | 4.47777i | −0.310493 | − | 0.225587i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.00000 | + | 0.726543i | −0.0502519 | + | 0.0365101i | ||||
\(397\) | 5.61803 | − | 4.08174i | 0.281961 | − | 0.204857i | −0.437811 | − | 0.899067i | \(-0.644246\pi\) |
0.719772 | + | 0.694210i | \(0.244246\pi\) | |||||||
\(398\) | 3.90983 | + | 12.0332i | 0.195982 | + | 0.603171i | ||||
\(399\) | −5.52786 | −0.276739 | ||||||||
\(400\) | −5.00000 | −0.250000 | ||||||||
\(401\) | −22.4508 | −1.12114 | −0.560571 | − | 0.828106i | \(-0.689418\pi\) | ||||
−0.560571 | + | 0.828106i | \(0.689418\pi\) | |||||||
\(402\) | 0.236068 | + | 0.726543i | 0.0117740 | + | 0.0362366i | ||||
\(403\) | −12.5623 | + | 9.12705i | −0.625773 | + | 0.454651i | ||||
\(404\) | 2.88197 | − | 2.09387i | 0.143383 | − | 0.104174i | ||||
\(405\) | −0.690983 | − | 2.12663i | −0.0343352 | − | 0.105673i | ||||
\(406\) | 23.9443 | + | 17.3965i | 1.18833 | + | 0.863375i | ||||
\(407\) | 3.81966 | 0.189334 | ||||||||
\(408\) | 9.35410 | + | 6.79615i | 0.463097 | + | 0.336460i | ||||
\(409\) | 0.371323 | − | 1.14281i | 0.0183607 | − | 0.0565085i | −0.941456 | − | 0.337135i | \(-0.890542\pi\) |
0.959817 | + | 0.280626i | \(0.0905422\pi\) | |||||||
\(410\) | −6.54508 | − | 4.75528i | −0.323239 | − | 0.234847i | ||||
\(411\) | −2.35410 | − | 7.24518i | −0.116119 | − | 0.357378i | ||||
\(412\) | −1.00000 | + | 3.07768i | −0.0492665 | + | 0.151627i | ||||
\(413\) | 5.52786 | − | 17.0130i | 0.272008 | − | 0.837156i | ||||
\(414\) | 1.38197 | + | 4.25325i | 0.0679199 | + | 0.209036i | ||||
\(415\) | −8.61803 | − | 26.5236i | −0.423043 | − | 1.30199i | ||||
\(416\) | 8.68034 | − | 26.7153i | 0.425589 | − | 1.30983i | ||||
\(417\) | 18.5623 | + | 13.4863i | 0.909000 | + | 0.660427i | ||||
\(418\) | −1.52786 | −0.0747303 | ||||||||
\(419\) | −12.1803 | − | 8.84953i | −0.595049 | − | 0.432328i | 0.249069 | − | 0.968486i | \(-0.419875\pi\) |
−0.844118 | + | 0.536158i | \(0.819875\pi\) | |||||||
\(420\) | 8.09017 | − | 5.87785i | 0.394760 | − | 0.286810i | ||||
\(421\) | −24.1525 | + | 17.5478i | −1.17712 | + | 0.855227i | −0.991844 | − | 0.127459i | \(-0.959318\pi\) |
−0.185276 | + | 0.982687i | \(0.559318\pi\) | |||||||
\(422\) | −14.4721 | + | 10.5146i | −0.704493 | + | 0.511844i | ||||
\(423\) | −0.236068 | − | 0.726543i | −0.0114780 | − | 0.0353257i | ||||
\(424\) | −10.8541 | −0.527122 | ||||||||
\(425\) | 5.95492 | − | 18.3273i | 0.288856 | − | 0.889007i | ||||
\(426\) | −5.23607 | −0.253688 | ||||||||
\(427\) | −2.23607 | − | 6.88191i | −0.108211 | − | 0.333039i | ||||
\(428\) | 6.09017 | − | 4.42477i | 0.294379 | − | 0.213879i | ||||
\(429\) | 5.61803 | − | 4.08174i | 0.271241 | − | 0.197068i | ||||
\(430\) | −5.32624 | + | 16.3925i | −0.256854 | + | 0.790515i | ||||
\(431\) | −16.7082 | − | 12.1392i | −0.804806 | − | 0.584726i | 0.107514 | − | 0.994204i | \(-0.465711\pi\) |
−0.912320 | + | 0.409478i | \(0.865711\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 17.7812 | + | 12.9188i | 0.854508 | + | 0.620836i | 0.926385 | − | 0.376577i | \(-0.122899\pi\) |
−0.0718775 | + | 0.997413i | \(0.522899\pi\) | |||||||
\(434\) | −3.81966 | + | 11.7557i | −0.183350 | + | 0.564292i | ||||
\(435\) | 11.9721 | − | 8.69827i | 0.574020 | − | 0.417050i | ||||
\(436\) | 2.44427 | + | 7.52270i | 0.117059 | + | 0.360272i | ||||
\(437\) | 1.70820 | − | 5.25731i | 0.0817145 | − | 0.251491i | ||||
\(438\) | −2.50000 | + | 7.69421i | −0.119455 | + | 0.367644i | ||||
\(439\) | 5.00000 | + | 15.3884i | 0.238637 | + | 0.734449i | 0.996618 | + | 0.0821726i | \(0.0261859\pi\) |
−0.757981 | + | 0.652276i | \(0.773814\pi\) | |||||||
\(440\) | 6.70820 | − | 4.87380i | 0.319801 | − | 0.232349i | ||||
\(441\) | 4.01722 | − | 12.3637i | 0.191296 | − | 0.588749i | ||||
\(442\) | −17.5172 | − | 12.7270i | −0.833209 | − | 0.605362i | ||||
\(443\) | −35.2361 | −1.67412 | −0.837058 | − | 0.547114i | \(-0.815726\pi\) | ||||
−0.837058 | + | 0.547114i | \(0.815726\pi\) | |||||||
\(444\) | −2.50000 | − | 1.81636i | −0.118645 | − | 0.0862005i | ||||
\(445\) | −3.71885 | + | 11.4454i | −0.176290 | + | 0.542566i | ||||
\(446\) | −6.61803 | + | 4.80828i | −0.313373 | + | 0.227679i | ||||
\(447\) | 15.2533 | − | 11.0822i | 0.721456 | − | 0.524168i | ||||
\(448\) | −9.67376 | − | 29.7728i | −0.457042 | − | 1.40663i | ||||
\(449\) | 16.7984 | 0.792764 | 0.396382 | − | 0.918086i | \(-0.370266\pi\) | ||||
0.396382 | + | 0.918086i | \(0.370266\pi\) | |||||||
\(450\) | 1.54508 | + | 4.75528i | 0.0728360 | + | 0.224166i | ||||
\(451\) | 4.47214 | 0.210585 | ||||||||
\(452\) | −5.66312 | − | 17.4293i | −0.266371 | − | 0.819805i | ||||
\(453\) | −6.09017 | + | 4.42477i | −0.286141 | + | 0.207894i | ||||
\(454\) | 16.1803 | − | 11.7557i | 0.759381 | − | 0.551723i | ||||
\(455\) | −45.4508 | + | 33.0220i | −2.13077 | + | 1.54809i | ||||
\(456\) | 3.00000 | + | 2.17963i | 0.140488 | + | 0.102070i | ||||
\(457\) | −22.3607 | −1.04599 | −0.522994 | − | 0.852336i | \(-0.675185\pi\) | ||||
−0.522994 | + | 0.852336i | \(0.675185\pi\) | |||||||
\(458\) | −17.7812 | − | 12.9188i | −0.830859 | − | 0.603654i | ||||
\(459\) | 1.19098 | − | 3.66547i | 0.0555903 | − | 0.171089i | ||||
\(460\) | 3.09017 | + | 9.51057i | 0.144080 | + | 0.443432i | ||||
\(461\) | −10.1353 | − | 31.1931i | −0.472046 | − | 1.45281i | −0.849901 | − | 0.526943i | \(-0.823338\pi\) |
0.377855 | − | 0.925865i | \(-0.376662\pi\) | |||||||
\(462\) | 1.70820 | − | 5.25731i | 0.0794728 | − | 0.244592i | ||||
\(463\) | 5.79837 | − | 17.8456i | 0.269473 | − | 0.829353i | −0.721156 | − | 0.692773i | \(-0.756389\pi\) |
0.990629 | − | 0.136580i | \(-0.0436112\pi\) | |||||||
\(464\) | −2.04508 | − | 6.29412i | −0.0949407 | − | 0.292197i | ||||
\(465\) | 5.00000 | + | 3.63271i | 0.231869 | + | 0.168463i | ||||
\(466\) | 3.82624 | − | 11.7759i | 0.177247 | − | 0.545510i | ||||
\(467\) | −22.7984 | − | 16.5640i | −1.05498 | − | 0.766490i | −0.0818293 | − | 0.996646i | \(-0.526076\pi\) |
−0.973154 | + | 0.230156i | \(0.926076\pi\) | |||||||
\(468\) | −5.61803 | −0.259694 | ||||||||
\(469\) | 2.76393 | + | 2.00811i | 0.127627 | + | 0.0927261i | ||||
\(470\) | 0.527864 | + | 1.62460i | 0.0243486 | + | 0.0749371i | ||||
\(471\) | −8.73607 | + | 6.34712i | −0.402537 | + | 0.292460i | ||||
\(472\) | −9.70820 | + | 7.05342i | −0.446856 | + | 0.324660i | ||||
\(473\) | −2.94427 | − | 9.06154i | −0.135378 | − | 0.416650i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.90983 | − | 5.87785i | 0.0876290 | − | 0.269694i | ||||
\(476\) | 17.2361 | 0.790014 | ||||||||
\(477\) | 1.11803 | + | 3.44095i | 0.0511913 | + | 0.157550i | ||||
\(478\) | 20.1803 | − | 14.6619i | 0.923027 | − | 0.670619i | ||||
\(479\) | −15.3262 | + | 11.1352i | −0.700274 | + | 0.508779i | −0.880021 | − | 0.474934i | \(-0.842472\pi\) |
0.179748 | + | 0.983713i | \(0.442472\pi\) | |||||||
\(480\) | −11.1803 | −0.510310 | ||||||||
\(481\) | 14.0451 | + | 10.2044i | 0.640401 | + | 0.465278i | ||||
\(482\) | 28.0344 | 1.27693 | ||||||||
\(483\) | 16.1803 | + | 11.7557i | 0.736231 | + | 0.534903i | ||||
\(484\) | 2.92705 | − | 9.00854i | 0.133048 | − | 0.409479i | ||||
\(485\) | −4.79837 | −0.217883 | ||||||||
\(486\) | 0.309017 | + | 0.951057i | 0.0140173 | + | 0.0431408i | ||||
\(487\) | 3.00000 | − | 9.23305i | 0.135943 | − | 0.418389i | −0.859793 | − | 0.510644i | \(-0.829407\pi\) |
0.995736 | + | 0.0922541i | \(0.0294072\pi\) | |||||||
\(488\) | −1.50000 | + | 4.61653i | −0.0679018 | + | 0.208980i | ||||
\(489\) | −4.61803 | − | 14.2128i | −0.208835 | − | 0.642727i | ||||
\(490\) | −8.98278 | + | 27.6462i | −0.405801 | + | 1.24893i | ||||
\(491\) | 1.81966 | − | 5.60034i | 0.0821201 | − | 0.252740i | −0.901563 | − | 0.432647i | \(-0.857580\pi\) |
0.983684 | + | 0.179907i | \(0.0575797\pi\) | |||||||
\(492\) | −2.92705 | − | 2.12663i | −0.131962 | − | 0.0958758i | ||||
\(493\) | 25.5066 | 1.14876 | ||||||||
\(494\) | −5.61803 | − | 4.08174i | −0.252767 | − | 0.183646i | ||||
\(495\) | −2.23607 | − | 1.62460i | −0.100504 | − | 0.0730203i | ||||
\(496\) | 2.23607 | − | 1.62460i | 0.100402 | − | 0.0729466i | ||||
\(497\) | −18.9443 | + | 13.7638i | −0.849767 | + | 0.617392i | ||||
\(498\) | 3.85410 | + | 11.8617i | 0.172706 | + | 0.531536i | ||||
\(499\) | −6.00000 | −0.268597 | −0.134298 | − | 0.990941i | \(-0.542878\pi\) | ||||
−0.134298 | + | 0.990941i | \(0.542878\pi\) | |||||||
\(500\) | 3.45492 | + | 10.6331i | 0.154508 | + | 0.475528i | ||||
\(501\) | 3.41641 | 0.152634 | ||||||||
\(502\) | −2.79837 | − | 8.61251i | −0.124898 | − | 0.384395i | ||||
\(503\) | −6.94427 | + | 5.04531i | −0.309630 | + | 0.224959i | −0.731738 | − | 0.681586i | \(-0.761290\pi\) |
0.422108 | + | 0.906546i | \(0.361290\pi\) | |||||||
\(504\) | −10.8541 | + | 7.88597i | −0.483480 | + | 0.351269i | ||||
\(505\) | 6.44427 | + | 4.68204i | 0.286766 | + | 0.208348i | ||||
\(506\) | 4.47214 | + | 3.24920i | 0.198811 | + | 0.144444i | ||||
\(507\) | 18.5623 | 0.824381 | ||||||||
\(508\) | −3.00000 | − | 2.17963i | −0.133103 | − | 0.0967053i | ||||
\(509\) | 6.22542 | − | 19.1599i | 0.275937 | − | 0.849247i | −0.713033 | − | 0.701131i | \(-0.752679\pi\) |
0.988970 | − | 0.148116i | \(-0.0473210\pi\) | |||||||
\(510\) | −2.66312 | + | 8.19624i | −0.117925 | + | 0.362935i | ||||
\(511\) | 11.1803 | + | 34.4095i | 0.494589 | + | 1.52219i | ||||
\(512\) | −3.39919 | + | 10.4616i | −0.150224 | + | 0.462343i | ||||
\(513\) | 0.381966 | − | 1.17557i | 0.0168642 | − | 0.0519027i | ||||
\(514\) | 3.64590 | + | 11.2209i | 0.160814 | + | 0.494934i | ||||
\(515\) | −7.23607 | −0.318859 | ||||||||
\(516\) | −2.38197 | + | 7.33094i | −0.104860 | + | 0.322727i | ||||
\(517\) | −0.763932 | − | 0.555029i | −0.0335977 | − | 0.0244102i | ||||
\(518\) | 13.8197 | 0.607201 | ||||||||
\(519\) | −17.0623 | − | 12.3965i | −0.748952 | − | 0.544146i | ||||
\(520\) | 37.6869 | 1.65268 | ||||||||
\(521\) | 21.8713 | − | 15.8904i | 0.958200 | − | 0.696173i | 0.00546804 | − | 0.999985i | \(-0.498259\pi\) |
0.952732 | + | 0.303812i | \(0.0982595\pi\) | |||||||
\(522\) | −5.35410 | + | 3.88998i | −0.234343 | + | 0.170260i | ||||
\(523\) | −7.94427 | − | 24.4500i | −0.347379 | − | 1.06912i | −0.960298 | − | 0.278976i | \(-0.910005\pi\) |
0.612919 | − | 0.790146i | \(-0.289995\pi\) | |||||||
\(524\) | 8.18034 | 0.357360 | ||||||||
\(525\) | 18.0902 | + | 13.1433i | 0.789520 | + | 0.573620i | ||||
\(526\) | −23.8885 | −1.04159 | ||||||||
\(527\) | 3.29180 | + | 10.1311i | 0.143393 | + | 0.441318i | ||||
\(528\) | −1.00000 | + | 0.726543i | −0.0435194 | + | 0.0316187i | ||||
\(529\) | 2.42705 | − | 1.76336i | 0.105524 | − | 0.0766676i | ||||
\(530\) | −2.50000 | − | 7.69421i | −0.108593 | − | 0.334215i | ||||
\(531\) | 3.23607 | + | 2.35114i | 0.140433 | + | 0.102031i | ||||
\(532\) | 5.52786 | 0.239663 | ||||||||
\(533\) | 16.4443 | + | 11.9475i | 0.712280 | + | 0.517502i | ||||
\(534\) | 1.66312 | − | 5.11855i | 0.0719702 | − | 0.221501i | ||||
\(535\) | 13.6180 | + | 9.89408i | 0.588759 | + | 0.427758i | ||||
\(536\) | −0.708204 | − | 2.17963i | −0.0305898 | − | 0.0941456i | ||||
\(537\) | −5.00000 | + | 15.3884i | −0.215766 | + | 0.664059i | ||||
\(538\) | −2.11803 | + | 6.51864i | −0.0913149 | + | 0.281038i | ||||
\(539\) | −4.96556 | − | 15.2824i | −0.213882 | − | 0.658260i | ||||
\(540\) | 0.690983 | + | 2.12663i | 0.0297352 | + | 0.0915155i | ||||
\(541\) | −6.07953 | + | 18.7109i | −0.261379 | + | 0.804443i | 0.731126 | + | 0.682242i | \(0.238995\pi\) |
−0.992505 | + | 0.122200i | \(0.961005\pi\) | |||||||
\(542\) | 0.145898 | + | 0.106001i | 0.00626686 | + | 0.00455314i | ||||
\(543\) | 14.7984 | 0.635059 | ||||||||
\(544\) | −15.5902 | − | 11.3269i | −0.668423 | − | 0.485638i | ||||
\(545\) | −14.3090 | + | 10.3961i | −0.612931 | + | 0.445320i | ||||
\(546\) | 20.3262 | − | 14.7679i | 0.869883 | − | 0.632007i | ||||
\(547\) | −34.2705 | + | 24.8990i | −1.46530 | + | 1.06460i | −0.483359 | + | 0.875422i | \(0.660583\pi\) |
−0.981942 | + | 0.189181i | \(0.939417\pi\) | |||||||
\(548\) | 2.35410 | + | 7.24518i | 0.100562 | + | 0.309499i | ||||
\(549\) | 1.61803 | 0.0690560 | ||||||||
\(550\) | 5.00000 | + | 3.63271i | 0.213201 | + | 0.154899i | ||||
\(551\) | 8.18034 | 0.348494 | ||||||||
\(552\) | −4.14590 | − | 12.7598i | −0.176461 | − | 0.543092i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −15.2082 | + | 11.0494i | −0.646135 | + | 0.469444i | ||||
\(555\) | 2.13525 | − | 6.57164i | 0.0906365 | − | 0.278951i | ||||
\(556\) | −18.5623 | − | 13.4863i | −0.787217 | − | 0.571947i | ||||
\(557\) | −11.2705 | −0.477547 | −0.238773 | − | 0.971075i | \(-0.576745\pi\) | ||||
−0.238773 | + | 0.971075i | \(0.576745\pi\) | |||||||
\(558\) | −2.23607 | − | 1.62460i | −0.0946603 | − | 0.0687747i | ||||
\(559\) | 13.3820 | − | 41.1855i | 0.565997 | − | 1.74196i | ||||
\(560\) | 8.09017 | − | 5.87785i | 0.341872 | − | 0.248385i | ||||
\(561\) | −1.47214 | − | 4.53077i | −0.0621536 | − | 0.191289i | ||||
\(562\) | −6.06231 | + | 18.6579i | −0.255723 | + | 0.787034i | ||||
\(563\) | −8.18034 | + | 25.1765i | −0.344760 | + | 1.06106i | 0.616952 | + | 0.787001i | \(0.288367\pi\) |
−0.961712 | + | 0.274062i | \(0.911633\pi\) | |||||||
\(564\) | 0.236068 | + | 0.726543i | 0.00994026 | + | 0.0305930i | ||||
\(565\) | 33.1525 | − | 24.0867i | 1.39474 | − | 1.01333i | ||||
\(566\) | 4.23607 | − | 13.0373i | 0.178055 | − | 0.547998i | ||||
\(567\) | 3.61803 | + | 2.62866i | 0.151943 | + | 0.110393i | ||||
\(568\) | 15.7082 | 0.659102 | ||||||||
\(569\) | −2.64590 | − | 1.92236i | −0.110922 | − | 0.0805894i | 0.530942 | − | 0.847408i | \(-0.321838\pi\) |
−0.641863 | + | 0.766819i | \(0.721838\pi\) | |||||||
\(570\) | −0.854102 | + | 2.62866i | −0.0357744 | + | 0.110102i | ||||
\(571\) | 13.5623 | − | 9.85359i | 0.567565 | − | 0.412360i | −0.266655 | − | 0.963792i | \(-0.585918\pi\) |
0.834220 | + | 0.551432i | \(0.185918\pi\) | |||||||
\(572\) | −5.61803 | + | 4.08174i | −0.234902 | + | 0.170666i | ||||
\(573\) | 2.05573 | + | 6.32688i | 0.0858793 | + | 0.264309i | ||||
\(574\) | 16.1803 | 0.675354 | ||||||||
\(575\) | −18.0902 | + | 13.1433i | −0.754412 | + | 0.548113i | ||||
\(576\) | 7.00000 | 0.291667 | ||||||||
\(577\) | −4.03444 | − | 12.4167i | −0.167956 | − | 0.516915i | 0.831286 | − | 0.555845i | \(-0.187605\pi\) |
−0.999242 | + | 0.0389296i | \(0.987605\pi\) | |||||||
\(578\) | 1.73607 | − | 1.26133i | 0.0722109 | − | 0.0524643i | ||||
\(579\) | −18.8713 | + | 13.7108i | −0.784265 | + | 0.569802i | ||||
\(580\) | −11.9721 | + | 8.69827i | −0.497116 | + | 0.361176i | ||||
\(581\) | 45.1246 | + | 32.7849i | 1.87208 | + | 1.36015i | ||||
\(582\) | 2.14590 | 0.0889503 | ||||||||
\(583\) | 3.61803 | + | 2.62866i | 0.149844 | + | 0.108868i | ||||
\(584\) | 7.50000 | − | 23.0826i | 0.310352 | − | 0.955166i | ||||
\(585\) | −3.88197 | − | 11.9475i | −0.160500 | − | 0.493967i | ||||
\(586\) | −6.42705 | − | 19.7804i | −0.265499 | − | 0.817122i | ||||
\(587\) | −12.7984 | + | 39.3893i | −0.528245 | + | 1.62577i | 0.229562 | + | 0.973294i | \(0.426271\pi\) |
−0.757807 | + | 0.652478i | \(0.773729\pi\) | |||||||
\(588\) | −4.01722 | + | 12.3637i | −0.165667 | + | 0.509872i | ||||
\(589\) | 1.05573 | + | 3.24920i | 0.0435005 | + | 0.133881i | ||||
\(590\) | −7.23607 | − | 5.25731i | −0.297904 | − | 0.216440i | ||||
\(591\) | 2.35410 | − | 7.24518i | 0.0968348 | − | 0.298027i | ||||
\(592\) | −2.50000 | − | 1.81636i | −0.102749 | − | 0.0746518i | ||||
\(593\) | 9.74265 | 0.400083 | 0.200041 | − | 0.979787i | \(-0.435892\pi\) | ||||
0.200041 | + | 0.979787i | \(0.435892\pi\) | |||||||
\(594\) | 1.00000 | + | 0.726543i | 0.0410305 | + | 0.0298104i | ||||
\(595\) | 11.9098 | + | 36.6547i | 0.488255 | + | 1.50270i | ||||
\(596\) | −15.2533 | + | 11.0822i | −0.624799 | + | 0.453943i | ||||
\(597\) | −10.2361 | + | 7.43694i | −0.418934 | + | 0.304374i | ||||
\(598\) | 7.76393 | + | 23.8949i | 0.317491 | + | 0.977136i | ||||
\(599\) | −3.52786 | −0.144145 | −0.0720723 | − | 0.997399i | \(-0.522961\pi\) | ||||
−0.0720723 | + | 0.997399i | \(0.522961\pi\) | |||||||
\(600\) | −4.63525 | − | 14.2658i | −0.189233 | − | 0.582401i | ||||
\(601\) | −8.67376 | −0.353810 | −0.176905 | − | 0.984228i | \(-0.556609\pi\) | ||||
−0.176905 | + | 0.984228i | \(0.556609\pi\) | |||||||
\(602\) | −10.6525 | − | 32.7849i | −0.434163 | − | 1.33621i | ||||
\(603\) | −0.618034 | + | 0.449028i | −0.0251683 | + | 0.0182858i | ||||
\(604\) | 6.09017 | − | 4.42477i | 0.247806 | − | 0.180041i | ||||
\(605\) | 21.1803 | 0.861103 | ||||||||
\(606\) | −2.88197 | − | 2.09387i | −0.117072 | − | 0.0850577i | ||||
\(607\) | −34.7639 | −1.41102 | −0.705512 | − | 0.708698i | \(-0.749283\pi\) | ||||
−0.705512 | + | 0.708698i | \(0.749283\pi\) | |||||||
\(608\) | −5.00000 | − | 3.63271i | −0.202777 | − | 0.147326i | ||||
\(609\) | −9.14590 | + | 28.1482i | −0.370610 | + | 1.14062i | ||||
\(610\) | −3.61803 | −0.146490 | ||||||||
\(611\) | −1.32624 | − | 4.08174i | −0.0536538 | − | 0.165130i | ||||
\(612\) | −1.19098 | + | 3.66547i | −0.0481426 | + | 0.148168i | ||||
\(613\) | 0.461493 | − | 1.42033i | 0.0186395 | − | 0.0573665i | −0.941304 | − | 0.337560i | \(-0.890399\pi\) |
0.959944 | + | 0.280193i | \(0.0903985\pi\) | |||||||
\(614\) | 10.0902 | + | 31.0543i | 0.407206 | + | 1.25325i | ||||
\(615\) | 2.50000 | − | 7.69421i | 0.100810 | − | 0.310260i | ||||
\(616\) | −5.12461 | + | 15.7719i | −0.206476 | + | 0.635469i | ||||
\(617\) | 16.1631 | + | 11.7432i | 0.650703 | + | 0.472763i | 0.863510 | − | 0.504331i | \(-0.168261\pi\) |
−0.212808 | + | 0.977094i | \(0.568261\pi\) | |||||||
\(618\) | 3.23607 | 0.130174 | ||||||||
\(619\) | 13.2361 | + | 9.61657i | 0.532002 | + | 0.386522i | 0.821106 | − | 0.570775i | \(-0.193357\pi\) |
−0.289104 | + | 0.957298i | \(0.593357\pi\) | |||||||
\(620\) | −5.00000 | − | 3.63271i | −0.200805 | − | 0.145893i | ||||
\(621\) | −3.61803 | + | 2.62866i | −0.145187 | + | 0.105484i | ||||
\(622\) | −14.3262 | + | 10.4086i | −0.574430 | + | 0.417348i | ||||
\(623\) | −7.43769 | − | 22.8909i | −0.297985 | − | 0.917103i | ||||
\(624\) | −5.61803 | −0.224901 | ||||||||
\(625\) | −20.2254 | + | 14.6946i | −0.809017 | + | 0.587785i | ||||
\(626\) | −0.472136 | −0.0188703 | ||||||||
\(627\) | −0.472136 | − | 1.45309i | −0.0188553 | − | 0.0580306i | ||||
\(628\) | 8.73607 | − | 6.34712i | 0.348607 | − | 0.253278i | ||||
\(629\) | 9.63525 | − | 7.00042i | 0.384183 | − | 0.279125i | ||||
\(630\) | −8.09017 | − | 5.87785i | −0.322320 | − | 0.234179i | ||||
\(631\) | −19.1803 | − | 13.9353i | −0.763557 | − | 0.554757i | 0.136442 | − | 0.990648i | \(-0.456433\pi\) |
−0.899999 | + | 0.435891i | \(0.856433\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.4721 | − | 10.5146i | −0.575216 | − | 0.417919i | ||||
\(634\) | 8.90983 | − | 27.4216i | 0.353855 | − | 1.08905i | ||||
\(635\) | 2.56231 | − | 7.88597i | 0.101682 | − | 0.312945i | ||||
\(636\) | −1.11803 | − | 3.44095i | −0.0443329 | − | 0.136443i | ||||
\(637\) | 22.5689 | − | 69.4599i | 0.894212 | − | 2.75210i | ||||
\(638\) | −2.52786 | + | 7.77997i | −0.100079 | + | 0.308012i | ||||
\(639\) | −1.61803 | − | 4.97980i | −0.0640084 | − | 0.196998i | ||||
\(640\) | 6.70820 | 0.265165 | ||||||||
\(641\) | 6.50658 | − | 20.0252i | 0.256994 | − | 0.790947i | −0.736436 | − | 0.676507i | \(-0.763493\pi\) |
0.993430 | − | 0.114440i | \(-0.0365073\pi\) | |||||||
\(642\) | −6.09017 | − | 4.42477i | −0.240360 | − | 0.174632i | ||||
\(643\) | −21.8885 | −0.863200 | −0.431600 | − | 0.902065i | \(-0.642051\pi\) | ||||
−0.431600 | + | 0.902065i | \(0.642051\pi\) | |||||||
\(644\) | −16.1803 | − | 11.7557i | −0.637595 | − | 0.463240i | ||||
\(645\) | −17.2361 | −0.678670 | ||||||||
\(646\) | −3.85410 | + | 2.80017i | −0.151638 | + | 0.110171i | ||||
\(647\) | 27.7984 | − | 20.1967i | 1.09287 | − | 0.794014i | 0.112986 | − | 0.993597i | \(-0.463959\pi\) |
0.979881 | + | 0.199582i | \(0.0639585\pi\) | |||||||
\(648\) | −0.927051 | − | 2.85317i | −0.0364180 | − | 0.112083i | ||||
\(649\) | 4.94427 | 0.194080 | ||||||||
\(650\) | 8.68034 | + | 26.7153i | 0.340471 | + | 1.04786i | ||||
\(651\) | −12.3607 | −0.484453 | ||||||||
\(652\) | 4.61803 | + | 14.2128i | 0.180856 | + | 0.556618i | ||||
\(653\) | 34.0623 | − | 24.7477i | 1.33296 | − | 0.968453i | 0.333289 | − | 0.942825i | \(-0.391841\pi\) |
0.999672 | − | 0.0256283i | \(-0.00815865\pi\) | |||||||
\(654\) | 6.39919 | − | 4.64928i | 0.250228 | − | 0.181801i | ||||
\(655\) | 5.65248 | + | 17.3965i | 0.220861 | + | 0.679739i | ||||
\(656\) | −2.92705 | − | 2.12663i | −0.114282 | − | 0.0830308i | ||||
\(657\) | −8.09017 | −0.315628 | ||||||||
\(658\) | −2.76393 | − | 2.00811i | −0.107749 | − | 0.0782844i | ||||
\(659\) | −10.3262 | + | 31.7809i | −0.402253 | + | 1.23801i | 0.520914 | + | 0.853609i | \(0.325591\pi\) |
−0.923167 | + | 0.384399i | \(0.874409\pi\) | |||||||
\(660\) | 2.23607 | + | 1.62460i | 0.0870388 | + | 0.0632374i | ||||
\(661\) | −0.437694 | − | 1.34708i | −0.0170243 | − | 0.0523955i | 0.942183 | − | 0.335097i | \(-0.108769\pi\) |
−0.959208 | + | 0.282702i | \(0.908769\pi\) | |||||||
\(662\) | −2.14590 | + | 6.60440i | −0.0834027 | + | 0.256687i | ||||
\(663\) | 6.69098 | − | 20.5927i | 0.259856 | − | 0.799755i | ||||
\(664\) | −11.5623 | − | 35.5851i | −0.448704 | − | 1.38097i | ||||
\(665\) | 3.81966 | + | 11.7557i | 0.148120 | + | 0.455867i | ||||
\(666\) | −0.954915 | + | 2.93893i | −0.0370022 | + | 0.113881i | ||||
\(667\) | −23.9443 | − | 17.3965i | −0.927126 | − | 0.673596i | ||||
\(668\) | −3.41641 | −0.132185 | ||||||||
\(669\) | −6.61803 | − | 4.80828i | −0.255868 | − | 0.185899i | ||||
\(670\) | 1.38197 | − | 1.00406i | 0.0533900 | − | 0.0387901i | ||||
\(671\) | 1.61803 | − | 1.17557i | 0.0624635 | − | 0.0453824i | ||||
\(672\) | 18.0902 | − | 13.1433i | 0.697843 | − | 0.507013i | ||||
\(673\) | 1.60739 | + | 4.94704i | 0.0619604 | + | 0.190694i | 0.977245 | − | 0.212113i | \(-0.0680345\pi\) |
−0.915285 | + | 0.402807i | \(0.868034\pi\) | |||||||
\(674\) | 2.94427 | 0.113409 | ||||||||
\(675\) | −4.04508 | + | 2.93893i | −0.155695 | + | 0.113119i | ||||
\(676\) | −18.5623 | −0.713935 | ||||||||
\(677\) | 3.27051 | + | 10.0656i | 0.125696 | + | 0.386852i | 0.994027 | − | 0.109132i | \(-0.0348072\pi\) |
−0.868331 | + | 0.495985i | \(0.834807\pi\) | |||||||
\(678\) | −14.8262 | + | 10.7719i | −0.569398 | + | 0.413692i | ||||
\(679\) | 7.76393 | − | 5.64083i | 0.297952 | − | 0.216475i | ||||
\(680\) | 7.98936 | − | 24.5887i | 0.306378 | − | 0.942934i | ||||
\(681\) | 16.1803 | + | 11.7557i | 0.620032 | + | 0.450480i | ||||
\(682\) | −3.41641 | −0.130821 | ||||||||
\(683\) | 15.7082 | + | 11.4127i | 0.601058 | + | 0.436694i | 0.846254 | − | 0.532779i | \(-0.178852\pi\) |
−0.245196 | + | 0.969473i | \(0.578852\pi\) | |||||||
\(684\) | −0.381966 | + | 1.17557i | −0.0146048 | + | 0.0449491i | ||||
\(685\) | −13.7812 | + | 10.0126i | −0.526551 | + | 0.382562i | ||||
\(686\) | −8.29180 | − | 25.5195i | −0.316582 | − | 0.974340i | ||||
\(687\) | 6.79180 | − | 20.9030i | 0.259123 | − | 0.797499i | ||||
\(688\) | −2.38197 | + | 7.33094i | −0.0908116 | + | 0.279489i | ||||
\(689\) | 6.28115 | + | 19.3314i | 0.239293 | + | 0.736468i | ||||
\(690\) | 8.09017 | − | 5.87785i | 0.307988 | − | 0.223766i | ||||
\(691\) | −5.18034 | + | 15.9434i | −0.197069 | + | 0.606517i | 0.802877 | + | 0.596145i | \(0.203302\pi\) |
−0.999946 | + | 0.0103723i | \(0.996698\pi\) | |||||||
\(692\) | 17.0623 | + | 12.3965i | 0.648612 | + | 0.471244i | ||||
\(693\) | 5.52786 | 0.209986 | ||||||||
\(694\) | 16.4164 | + | 11.9272i | 0.623158 | + | 0.452751i | ||||
\(695\) | 15.8541 | − | 48.7939i | 0.601380 | − | 1.85086i | ||||
\(696\) | 16.0623 | − | 11.6699i | 0.608840 | − | 0.442348i | ||||
\(697\) | 11.2812 | − | 8.19624i | 0.427304 | − | 0.310455i | ||||
\(698\) | −1.24671 | − | 3.83698i | −0.0471887 | − | 0.145232i | ||||
\(699\) | 12.3820 | 0.468329 | ||||||||
\(700\) | −18.0902 | − | 13.1433i | −0.683744 | − | 0.496769i | ||||
\(701\) | 20.5623 | 0.776628 | 0.388314 | − | 0.921527i | \(-0.373058\pi\) | ||||
0.388314 | + | 0.921527i | \(0.373058\pi\) | |||||||
\(702\) | 1.73607 | + | 5.34307i | 0.0655237 | + | 0.201661i | ||||
\(703\) | 3.09017 | − | 2.24514i | 0.116548 | − | 0.0846771i | ||||
\(704\) | 7.00000 | − | 5.08580i | 0.263822 | − | 0.191678i | ||||
\(705\) | −1.38197 | + | 1.00406i | −0.0520479 | + | 0.0378150i | ||||
\(706\) | −11.6180 | − | 8.44100i | −0.437250 | − | 0.317681i | ||||
\(707\) | −15.9311 | −0.599151 | ||||||||
\(708\) | −3.23607 | − | 2.35114i | −0.121619 | − | 0.0883613i | ||||
\(709\) | −12.4443 | + | 38.2995i | −0.467354 | + | 1.43837i | 0.388643 | + | 0.921389i | \(0.372944\pi\) |
−0.855997 | + | 0.516981i | \(0.827056\pi\) | |||||||
\(710\) | 3.61803 | + | 11.1352i | 0.135782 | + | 0.417895i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.98936 | + | 15.3557i | −0.186984 | + | 0.575478i | ||||
\(713\) | 3.81966 | − | 11.7557i | 0.143047 | − | 0.440255i | ||||
\(714\) | −5.32624 | − | 16.3925i | −0.199329 | − | 0.613473i | ||||
\(715\) | −12.5623 | − | 9.12705i | −0.469804 | − | 0.341332i | ||||
\(716\) | 5.00000 | − | 15.3884i | 0.186859 | − | 0.575092i | ||||
\(717\) | 20.1803 | + | 14.6619i | 0.753649 | + | 0.547558i | ||||
\(718\) | −37.4164 | −1.39637 | ||||||||
\(719\) | 0.0901699 | + | 0.0655123i | 0.00336277 | + | 0.00244320i | 0.589465 | − | 0.807794i | \(-0.299338\pi\) |
−0.586103 | + | 0.810237i | \(0.699338\pi\) | |||||||
\(720\) | 0.690983 | + | 2.12663i | 0.0257514 | + | 0.0792547i | ||||
\(721\) | 11.7082 | − | 8.50651i | 0.436036 | − | 0.316799i | ||||
\(722\) | 14.1353 | − | 10.2699i | 0.526060 | − | 0.382205i | ||||
\(723\) | 8.66312 | + | 26.6623i | 0.322185 | + | 0.991583i | ||||
\(724\) | −14.7984 | −0.549977 | ||||||||
\(725\) | −26.7705 | − | 19.4499i | −0.994232 | − | 0.722352i | ||||
\(726\) | −9.47214 | −0.351544 | ||||||||
\(727\) | 14.4164 | + | 44.3691i | 0.534675 | + | 1.64556i | 0.744350 | + | 0.667789i | \(0.232759\pi\) |
−0.209675 | + | 0.977771i | \(0.567241\pi\) | |||||||
\(728\) | −60.9787 | + | 44.3036i | −2.26002 | + | 1.64200i | ||||
\(729\) | −0.809017 | + | 0.587785i | −0.0299636 | + | 0.0217698i | ||||
\(730\) | 18.0902 | 0.669547 | ||||||||
\(731\) | −24.0344 | − | 17.4620i | −0.888946 | − | 0.645857i | ||||
\(732\) | −1.61803 | −0.0598043 | ||||||||
\(733\) | −23.7984 | − | 17.2905i | −0.879013 | − | 0.638640i | 0.0539772 | − | 0.998542i | \(-0.482810\pi\) |
−0.932990 | + | 0.359902i | \(0.882810\pi\) | |||||||
\(734\) | −1.85410 | + | 5.70634i | −0.0684362 | + | 0.210625i | ||||
\(735\) | −29.0689 | −1.07222 | ||||||||
\(736\) | 6.90983 | + | 21.2663i | 0.254700 | + | 0.783885i | ||||
\(737\) | −0.291796 | + | 0.898056i | −0.0107484 | + | 0.0330803i | ||||
\(738\) | −1.11803 | + | 3.44095i | −0.0411554 | + | 0.126663i | ||||
\(739\) | 1.32624 | + | 4.08174i | 0.0487865 | + | 0.150149i | 0.972482 | − | 0.232978i | \(-0.0748470\pi\) |
−0.923696 | + | 0.383127i | \(0.874847\pi\) | |||||||
\(740\) | −2.13525 | + | 6.57164i | −0.0784935 | + | 0.241578i | ||||
\(741\) | 2.14590 | − | 6.60440i | 0.0788315 | − | 0.242619i | ||||
\(742\) | 13.0902 | + | 9.51057i | 0.480555 | + | 0.349144i | ||||
\(743\) | 41.1246 | 1.50872 | 0.754358 | − | 0.656463i | \(-0.227948\pi\) | ||||
0.754358 | + | 0.656463i | \(0.227948\pi\) | |||||||
\(744\) | 6.70820 | + | 4.87380i | 0.245935 | + | 0.178682i | ||||
\(745\) | −34.1074 | − | 24.7805i | −1.24960 | − | 0.907886i | ||||
\(746\) | −2.09017 | + | 1.51860i | −0.0765266 | + | 0.0555998i | ||||
\(747\) | −10.0902 | + | 7.33094i | −0.369180 | + | 0.268225i | ||||
\(748\) | 1.47214 | + | 4.53077i | 0.0538266 | + | 0.165661i | ||||
\(749\) | −33.6656 | −1.23012 | ||||||||
\(750\) | 9.04508 | − | 6.57164i | 0.330280 | − | 0.239962i | ||||
\(751\) | 36.6525 | 1.33747 | 0.668734 | − | 0.743502i | \(-0.266837\pi\) | ||||
0.668734 | + | 0.743502i | \(0.266837\pi\) | |||||||
\(752\) | 0.236068 | + | 0.726543i | 0.00860851 | + | 0.0264943i | ||||
\(753\) | 7.32624 | − | 5.32282i | 0.266983 | − | 0.193974i | ||||
\(754\) | −30.0795 | + | 21.8541i | −1.09543 | + | 0.795878i | ||||
\(755\) | 13.6180 | + | 9.89408i | 0.495611 | + | 0.360082i | ||||
\(756\) | −3.61803 | − | 2.62866i | −0.131587 | − | 0.0956033i | ||||
\(757\) | 29.6180 | 1.07649 | 0.538243 | − | 0.842790i | \(-0.319088\pi\) | ||||
0.538243 | + | 0.842790i | \(0.319088\pi\) | |||||||
\(758\) | 2.76393 | + | 2.00811i | 0.100391 | + | 0.0729380i | ||||
\(759\) | −1.70820 | + | 5.25731i | −0.0620039 | + | 0.190828i | ||||
\(760\) | 2.56231 | − | 7.88597i | 0.0929446 | − | 0.286054i | ||||
\(761\) | 10.1180 | + | 31.1401i | 0.366778 | + | 1.12883i | 0.948860 | + | 0.315697i | \(0.102238\pi\) |
−0.582081 | + | 0.813130i | \(0.697762\pi\) | |||||||
\(762\) | −1.14590 | + | 3.52671i | −0.0415115 | + | 0.127759i | ||||
\(763\) | 10.9311 | − | 33.6425i | 0.395733 | − | 1.21794i | ||||
\(764\) | −2.05573 | − | 6.32688i | −0.0743736 | − | 0.228899i | ||||
\(765\) | −8.61803 | −0.311586 | ||||||||
\(766\) | −10.1459 | + | 31.2259i | −0.366586 | + | 1.12824i | ||||
\(767\) | 18.1803 | + | 13.2088i | 0.656454 | + | 0.476942i | ||||
\(768\) | −17.0000 | −0.613435 | ||||||||
\(769\) | 40.7426 | + | 29.6013i | 1.46922 | + | 1.06745i | 0.980840 | + | 0.194817i | \(0.0624112\pi\) |
0.488378 | + | 0.872632i | \(0.337589\pi\) | |||||||
\(770\) | −12.3607 | −0.445448 | ||||||||
\(771\) | −9.54508 | + | 6.93491i | −0.343758 | + | 0.249755i | ||||
\(772\) | 18.8713 | − | 13.7108i | 0.679194 | − | 0.493463i | ||||
\(773\) | 8.93769 | + | 27.5074i | 0.321467 | + | 0.989372i | 0.973010 | + | 0.230761i | \(0.0741216\pi\) |
−0.651544 | + | 0.758611i | \(0.725878\pi\) | |||||||
\(774\) | 7.70820 | 0.277066 | ||||||||
\(775\) | 4.27051 | − | 13.1433i | 0.153401 | − | 0.472120i | ||||
\(776\) | −6.43769 | −0.231100 | ||||||||
\(777\) | 4.27051 | + | 13.1433i | 0.153204 | + | 0.471512i | ||||
\(778\) | 20.9615 | − | 15.2294i | 0.751506 | − | 0.546001i | ||||
\(779\) | 3.61803 | − | 2.62866i | 0.129630 | − | 0.0941814i | ||||
\(780\) | 3.88197 | + | 11.9475i | 0.138997 | + | 0.427788i | ||||
\(781\) | −5.23607 | − | 3.80423i | −0.187361 | − | 0.136126i | ||||
\(782\) | 17.2361 | 0.616361 | ||||||||
\(783\) | −5.35410 | − | 3.88998i | −0.191340 | − | 0.139017i | ||||
\(784\) | −4.01722 | + | 12.3637i | −0.143472 | + | 0.441562i | ||||
\(785\) | 19.5344 | + | 14.1926i | 0.697214 | + | 0.506556i | ||||
\(786\) | −2.52786 | − | 7.77997i | −0.0901659 | − | 0.277502i | ||||
\(787\) | −4.38197 | + | 13.4863i | −0.156200 | + | 0.480735i | −0.998281 | − | 0.0586173i | \(-0.981331\pi\) |
0.842080 | + | 0.539352i | \(0.181331\pi\) | |||||||
\(788\) | −2.35410 | + | 7.24518i | −0.0838614 | + | 0.258099i | ||||
\(789\) | −7.38197 | − | 22.7194i | −0.262805 | − | 0.808830i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −25.3262 | + | 77.9461i | −0.900497 | + | 2.77145i | ||||
\(792\) | −3.00000 | − | 2.17963i | −0.106600 | − | 0.0774497i | ||||
\(793\) | 9.09017 | 0.322801 | ||||||||
\(794\) | 5.61803 | + | 4.08174i | 0.199377 | + | 0.144856i | ||||
\(795\) | 6.54508 | − | 4.75528i | 0.232130 | − | 0.168652i | ||||
\(796\) | 10.2361 | − | 7.43694i | 0.362808 | − | 0.263595i | ||||
\(797\) | 39.7254 | − | 28.8622i | 1.40715 | − | 1.02235i | 0.413417 | − | 0.910542i | \(-0.364335\pi\) |
0.993730 | − | 0.111810i | \(-0.0356649\pi\) | |||||||
\(798\) | −1.70820 | − | 5.25731i | −0.0604698 | − | 0.186107i | ||||
\(799\) | −2.94427 | −0.104161 | ||||||||
\(800\) | 7.72542 | + | 23.7764i | 0.273135 | + | 0.840623i | ||||
\(801\) | 5.38197 | 0.190162 | ||||||||
\(802\) | −6.93769 | − | 21.3520i | −0.244978 | − | 0.753966i | ||||
\(803\) | −8.09017 | + | 5.87785i | −0.285496 | + | 0.207425i | ||||
\(804\) | 0.618034 | − | 0.449028i | 0.0217964 | − | 0.0158360i | ||||
\(805\) | 13.8197 | − | 42.5325i | 0.487079 | − | 1.49908i | ||||
\(806\) | −12.5623 | − | 9.12705i | −0.442488 | − | 0.321487i | ||||
\(807\) | −6.85410 | −0.241276 | ||||||||
\(808\) | 8.64590 | + | 6.28161i | 0.304162 | + | 0.220986i | ||||
\(809\) | 8.71885 | − | 26.8339i | 0.306538 | − | 0.943428i | −0.672560 | − | 0.740042i | \(-0.734805\pi\) |
0.979099 | − | 0.203386i | \(-0.0651945\pi\) | |||||||
\(810\) | 1.80902 | − | 1.31433i | 0.0635624 | − | 0.0461808i | ||||
\(811\) | 1.47214 | + | 4.53077i | 0.0516937 | + | 0.159097i | 0.973571 | − | 0.228386i | \(-0.0733447\pi\) |
−0.921877 | + | 0.387483i | \(0.873345\pi\) | |||||||
\(812\) | 9.14590 | − | 28.1482i | 0.320958 | − | 0.987807i | ||||
\(813\) | −0.0557281 | + | 0.171513i | −0.00195447 | + | 0.00601524i | ||||
\(814\) | 1.18034 | + | 3.63271i | 0.0413709 | + | 0.127327i | ||||
\(815\) | −27.0344 | + | 19.6417i | −0.946975 | + | 0.688018i | ||||
\(816\) | −1.19098 | + | 3.66547i | −0.0416927 | + | 0.128317i | ||||
\(817\) | −7.70820 | − | 5.60034i | −0.269676 | − | 0.195931i | ||||
\(818\) | 1.20163 | 0.0420139 | ||||||||
\(819\) | 20.3262 | + | 14.7679i | 0.710256 | + | 0.516031i | ||||
\(820\) | −2.50000 | + | 7.69421i | −0.0873038 | + | 0.268693i | ||||
\(821\) | −18.5623 | + | 13.4863i | −0.647829 | + | 0.470675i | −0.862531 | − | 0.506004i | \(-0.831122\pi\) |
0.214702 | + | 0.976680i | \(0.431122\pi\) | |||||||
\(822\) | 6.16312 | − | 4.47777i | 0.214963 | − | 0.156180i | ||||
\(823\) | −5.94427 | − | 18.2946i | −0.207204 | − | 0.637709i | −0.999616 | − | 0.0277222i | \(-0.991175\pi\) |
0.792411 | − | 0.609987i | \(-0.208825\pi\) | |||||||
\(824\) | −9.70820 | −0.338201 | ||||||||
\(825\) | −1.90983 | + | 5.87785i | −0.0664917 | + | 0.204641i | ||||
\(826\) | 17.8885 | 0.622422 | ||||||||
\(827\) | −11.1459 | − | 34.3035i | −0.387581 | − | 1.19285i | −0.934591 | − | 0.355725i | \(-0.884234\pi\) |
0.547010 | − | 0.837126i | \(-0.315766\pi\) | |||||||
\(828\) | 3.61803 | − | 2.62866i | 0.125735 | − | 0.0913521i | ||||
\(829\) | −9.30902 | + | 6.76340i | −0.323316 | + | 0.234902i | −0.737589 | − | 0.675250i | \(-0.764036\pi\) |
0.414273 | + | 0.910152i | \(0.364036\pi\) | |||||||
\(830\) | 22.5623 | − | 16.3925i | 0.783149 | − | 0.568991i | ||||
\(831\) | −15.2082 | − | 11.0494i | −0.527567 | − | 0.383300i | ||||
\(832\) | 39.3262 | 1.36339 | ||||||||
\(833\) | −40.5344 | − | 29.4500i | −1.40444 | − | 1.02038i | ||||
\(834\) | −7.09017 | + | 21.8213i | −0.245513 | + | 0.755610i | ||||
\(835\) | −2.36068 | − | 7.26543i | −0.0816947 | − | 0.251430i | ||||
\(836\) | 0.472136 | + | 1.45309i | 0.0163292 | + | 0.0502560i | ||||
\(837\) | 0.854102 | − | 2.62866i | 0.0295221 | − | 0.0908596i | ||||
\(838\) | 4.65248 | − | 14.3188i | 0.160717 | − | 0.494636i | ||||
\(839\) | 4.34752 | + | 13.3803i | 0.150093 | + | 0.461939i | 0.997631 | − | 0.0687961i | \(-0.0219158\pi\) |
−0.847538 | + | 0.530735i | \(0.821916\pi\) | |||||||
\(840\) | 24.2705 | + | 17.6336i | 0.837412 | + | 0.608416i | ||||
\(841\) | 4.57295 | − | 14.0741i | 0.157688 | − | 0.485313i | ||||
\(842\) | −24.1525 | − | 17.5478i | −0.832349 | − | 0.604737i | ||||
\(843\) | −19.6180 | −0.675681 | ||||||||
\(844\) | 14.4721 | + | 10.5146i | 0.498151 | + | 0.361928i | ||||
\(845\) | −12.8262 | − | 39.4751i | −0.441236 | − | 1.35798i | ||||
\(846\) | 0.618034 | − | 0.449028i | 0.0212484 | − | 0.0154379i | ||||
\(847\) | −34.2705 | + | 24.8990i | −1.17755 | + | 0.855539i | ||||
\(848\) | −1.11803 | − | 3.44095i | −0.0383934 | − | 0.118163i | ||||
\(849\) | 13.7082 | 0.470464 | ||||||||
\(850\) | 19.2705 | 0.660973 | ||||||||
\(851\) | −13.8197 | −0.473732 | ||||||||
\(852\) | 1.61803 | + | 4.97980i | 0.0554329 | + | 0.170605i | ||||
\(853\) | −18.7254 | + | 13.6048i | −0.641146 | + | 0.465820i | −0.860244 | − | 0.509883i | \(-0.829689\pi\) |
0.219097 | + | 0.975703i | \(0.429689\pi\) | |||||||
\(854\) | 5.85410 | − | 4.25325i | 0.200323 | − | 0.145543i | ||||
\(855\) | −2.76393 | −0.0945245 | ||||||||
\(856\) | 18.2705 | + | 13.2743i | 0.624473 | + | 0.453706i | ||||
\(857\) | −12.4721 | −0.426040 | −0.213020 | − | 0.977048i | \(-0.568330\pi\) | ||||
−0.213020 | + | 0.977048i | \(0.568330\pi\) | |||||||
\(858\) | 5.61803 | + | 4.08174i | 0.191797 | + | 0.139348i | ||||
\(859\) | −7.23607 | + | 22.2703i | −0.246891 | + | 0.759854i | 0.748428 | + | 0.663216i | \(0.230809\pi\) |
−0.995320 | + | 0.0966379i | \(0.969191\pi\) | |||||||
\(860\) | 17.2361 | 0.587745 | ||||||||
\(861\) | 5.00000 | + | 15.3884i | 0.170400 | + | 0.524436i | ||||
\(862\) | 6.38197 | − | 19.6417i | 0.217371 | − | 0.668998i | ||||
\(863\) | 3.36068 | − | 10.3431i | 0.114399 | − | 0.352084i | −0.877422 | − | 0.479719i | \(-0.840739\pi\) |
0.991821 | + | 0.127635i | \(0.0407387\pi\) | |||||||
\(864\) | 1.54508 | + | 4.75528i | 0.0525649 | + | 0.161778i | ||||
\(865\) | −14.5729 | + | 44.8509i | −0.495495 | + | 1.52498i | ||||
\(866\) | −6.79180 | + | 20.9030i | −0.230795 | + | 0.710313i | ||||
\(867\) | 1.73607 | + | 1.26133i | 0.0589600 | + | 0.0428369i | ||||
\(868\) | 12.3607 | 0.419549 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 11.9721 | + | 8.69827i | 0.405893 | + | 0.294899i | ||||
\(871\) | −3.47214 | + | 2.52265i | −0.117649 | + | 0.0854769i | ||||
\(872\) | −19.1976 | + | 13.9478i | −0.650111 | + | 0.472334i | ||||
\(873\) | 0.663119 | + | 2.04087i | 0.0224432 | + | 0.0690730i | ||||
\(874\) | 5.52786 | 0.186983 | ||||||||
\(875\) | 15.4508 | − | 47.5528i | 0.522334 | − | 1.60758i | ||||
\(876\) | 8.09017 | 0.273342 | ||||||||
\(877\) | −10.2639 | − | 31.5891i | −0.346588 | − | 1.06669i | −0.960728 | − | 0.277492i | \(-0.910497\pi\) |
0.614140 | − | 0.789197i | \(-0.289503\pi\) | |||||||
\(878\) | −13.0902 | + | 9.51057i | −0.441772 | + | 0.320966i | ||||
\(879\) | 16.8262 | − | 12.2250i | 0.567535 | − | 0.412338i | ||||
\(880\) | 2.23607 | + | 1.62460i | 0.0753778 | + | 0.0547652i | ||||
\(881\) | −34.7426 | − | 25.2420i | −1.17051 | − | 0.850425i | −0.179440 | − | 0.983769i | \(-0.557428\pi\) |
−0.991070 | + | 0.133344i | \(0.957428\pi\) | |||||||
\(882\) | 13.0000 | 0.437733 | ||||||||
\(883\) | −17.9443 | − | 13.0373i | −0.603873 | − | 0.438739i | 0.243379 | − | 0.969931i | \(-0.421744\pi\) |
−0.847251 | + | 0.531192i | \(0.821744\pi\) | |||||||
\(884\) | −6.69098 | + | 20.5927i | −0.225042 | + | 0.692608i | ||||
\(885\) | 2.76393 | − | 8.50651i | 0.0929086 | − | 0.285943i | ||||
\(886\) | −10.8885 | − | 33.5115i | −0.365808 | − | 1.12584i | ||||
\(887\) | −7.14590 | + | 21.9928i | −0.239936 | + | 0.738446i | 0.756492 | + | 0.654002i | \(0.226911\pi\) |
−0.996428 | + | 0.0844440i | \(0.973089\pi\) | |||||||
\(888\) | 2.86475 | − | 8.81678i | 0.0961346 | − | 0.295872i | ||||
\(889\) | 5.12461 | + | 15.7719i | 0.171874 | + | 0.528974i | ||||
\(890\) | −12.0344 | −0.403395 | ||||||||
\(891\) | −0.381966 | + | 1.17557i | −0.0127963 | + | 0.0393831i | ||||
\(892\) | 6.61803 | + | 4.80828i | 0.221588 | + | 0.160993i | ||||
\(893\) | −0.944272 | −0.0315989 | ||||||||
\(894\) | 15.2533 | + | 11.0822i | 0.510146 | + | 0.370643i | ||||
\(895\) | 36.1803 | 1.20938 | ||||||||
\(896\) | −10.8541 | + | 7.88597i | −0.362610 | + | 0.263452i | ||||
\(897\) | −20.3262 | + | 14.7679i | −0.678673 | + | 0.493085i | ||||
\(898\) | 5.19098 | + | 15.9762i | 0.173225 | + | 0.533133i | ||||
\(899\) | 18.2918 | 0.610066 | ||||||||
\(900\) | 4.04508 | − | 2.93893i | 0.134836 | − | 0.0979642i | ||||
\(901\) | 13.9443 | 0.464551 | ||||||||
\(902\) | 1.38197 | + | 4.25325i | 0.0460144 | + | 0.141618i | ||||
\(903\) | 27.8885 | − | 20.2622i | 0.928073 | − | 0.674284i | ||||
\(904\) | 44.4787 | − | 32.3157i | 1.47934 | − | 1.07480i | ||||
\(905\) | −10.2254 | − | 31.4706i | −0.339905 | − | 1.04612i | ||||
\(906\) | −6.09017 | − | 4.42477i | −0.202332 | − | 0.147003i | ||||
\(907\) | 7.12461 | 0.236569 | 0.118284 | − | 0.992980i | \(-0.462261\pi\) | ||||
0.118284 | + | 0.992980i | \(0.462261\pi\) | |||||||
\(908\) | −16.1803 | − | 11.7557i | −0.536963 | − | 0.390127i | ||||
\(909\) | 1.10081 | − | 3.38795i | 0.0365117 | − | 0.112371i | ||||
\(910\) | −45.4508 | − | 33.0220i | −1.50668 | − | 1.09467i | ||||
\(911\) | 5.61803 | + | 17.2905i | 0.186134 | + | 0.572861i | 0.999966 | − | 0.00823898i | \(-0.00262258\pi\) |
−0.813832 | + | 0.581100i | \(0.802623\pi\) | |||||||
\(912\) | −0.381966 | + | 1.17557i | −0.0126482 | + | 0.0389270i | ||||
\(913\) | −4.76393 | + | 14.6619i | −0.157663 | + | 0.485237i | ||||
\(914\) | −6.90983 | − | 21.2663i | −0.228557 | − | 0.703426i | ||||
\(915\) | −1.11803 | − | 3.44095i | −0.0369611 | − | 0.113754i | ||||
\(916\) | −6.79180 | + | 20.9030i | −0.224407 | + | 0.690655i | ||||
\(917\) | −29.5967 | − | 21.5033i | −0.977371 | − | 0.710101i | ||||
\(918\) | 3.85410 | 0.127204 | ||||||||
\(919\) | −39.7984 | − | 28.9152i | −1.31283 | − | 0.953825i | −0.999992 | − | 0.00401741i | \(-0.998721\pi\) |
−0.312835 | − | 0.949807i | \(-0.601279\pi\) | |||||||
\(920\) | −24.2705 | + | 17.6336i | −0.800175 | + | 0.581361i | ||||
\(921\) | −26.4164 | + | 19.1926i | −0.870450 | + | 0.632419i | ||||
\(922\) | 26.5344 | − | 19.2784i | 0.873865 | − | 0.634900i | ||||
\(923\) | −9.09017 | − | 27.9767i | −0.299207 | − | 0.920863i | ||||
\(924\) | −5.52786 | −0.181853 | ||||||||
\(925\) | −15.4508 | −0.508021 | ||||||||
\(926\) | 18.7639 | 0.616621 | ||||||||
\(927\) | 1.00000 | + | 3.07768i | 0.0328443 | + | 0.101084i | ||||
\(928\) | −26.7705 | + | 19.4499i | −0.878785 | + | 0.638475i | ||||
\(929\) | 7.35410 | − | 5.34307i | 0.241280 | − | 0.175300i | −0.460573 | − | 0.887622i | \(-0.652356\pi\) |
0.701853 | + | 0.712321i | \(0.252356\pi\) | |||||||
\(930\) | −1.90983 | + | 5.87785i | −0.0626258 | + | 0.192742i | ||||
\(931\) | −13.0000 | − | 9.44505i | −0.426058 | − | 0.309549i | ||||
\(932\) | −12.3820 | −0.405585 | ||||||||
\(933\) | −14.3262 | − | 10.4086i | −0.469020 | − | 0.340763i | ||||
\(934\) | 8.70820 | − | 26.8011i | 0.284941 | − | 0.876959i | ||||
\(935\) | −8.61803 | + | 6.26137i | −0.281840 | + | 0.204769i | ||||
\(936\) | −5.20820 | − | 16.0292i | −0.170235 | − | 0.523931i | ||||
\(937\) | −15.0451 | + | 46.3040i | −0.491502 | + | 1.51269i | 0.330837 | + | 0.943688i | \(0.392669\pi\) |
−0.822339 | + | 0.568998i | \(0.807331\pi\) | |||||||
\(938\) | −1.05573 | + | 3.24920i | −0.0344707 | + | 0.106090i | ||||
\(939\) | −0.145898 | − | 0.449028i | −0.00476120 | − | 0.0146535i | ||||
\(940\) | 1.38197 | − | 1.00406i | 0.0450748 | − | 0.0327487i | ||||
\(941\) | −3.19098 | + | 9.82084i | −0.104023 | + | 0.320150i | −0.989500 | − | 0.144533i | \(-0.953832\pi\) |
0.885477 | + | 0.464683i | \(0.153832\pi\) | |||||||
\(942\) | −8.73607 | − | 6.34712i | −0.284636 | − | 0.206801i | ||||
\(943\) | −16.1803 | −0.526904 | ||||||||
\(944\) | −3.23607 | − | 2.35114i | −0.105325 | − | 0.0765231i | ||||
\(945\) | 3.09017 | − | 9.51057i | 0.100523 | − | 0.309379i | ||||
\(946\) | 7.70820 | − | 5.60034i | 0.250615 | − | 0.182083i | ||||
\(947\) | −2.09017 | + | 1.51860i | −0.0679214 | + | 0.0493478i | −0.621228 | − | 0.783630i | \(-0.713366\pi\) |
0.553306 | + | 0.832978i | \(0.313366\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −45.4508 | −1.47540 | ||||||||
\(950\) | 6.18034 | 0.200517 | ||||||||
\(951\) | 28.8328 | 0.934968 | ||||||||
\(952\) | 15.9787 | + | 49.1774i | 0.517873 | + | 1.59385i | ||||
\(953\) | 0.881966 | − | 0.640786i | 0.0285697 | − | 0.0207571i | −0.573409 | − | 0.819269i | \(-0.694379\pi\) |
0.601978 | + | 0.798512i | \(0.294379\pi\) | |||||||
\(954\) | −2.92705 | + | 2.12663i | −0.0947668 | + | 0.0688521i | ||||
\(955\) | 12.0344 | − | 8.74353i | 0.389425 | − | 0.282934i | ||||
\(956\) | −20.1803 | − | 14.6619i | −0.652679 | − | 0.474199i | ||||
\(957\) | −8.18034 | −0.264433 | ||||||||
\(958\) | −15.3262 | − | 11.1352i | −0.495168 | − | 0.359761i | ||||
\(959\) | 10.5279 | − | 32.4014i | 0.339962 | − | 1.04630i | ||||
\(960\) | −4.83688 | − | 14.8864i | −0.156110 | − | 0.480456i | ||||
\(961\) | −7.21885 | − | 22.2173i | −0.232866 | − | 0.716688i | ||||
\(962\) | −5.36475 | + | 16.5110i | −0.172966 | + | 0.532336i | ||||
\(963\) | 2.32624 | − | 7.15942i | 0.0749620 | − | 0.230709i | ||||
\(964\) | −8.66312 | − | 26.6623i | −0.279020 | − | 0.858736i | ||||
\(965\) | 42.1976 | + | 30.6583i | 1.35839 | + | 0.986926i | ||||
\(966\) | −6.18034 | + | 19.0211i | −0.198849 | + | 0.611995i | ||||
\(967\) | 15.2361 | + | 11.0697i | 0.489959 | + | 0.355976i | 0.805169 | − | 0.593046i | \(-0.202075\pi\) |
−0.315210 | + | 0.949022i | \(0.602075\pi\) | |||||||
\(968\) | 28.4164 | 0.913338 | ||||||||
\(969\) | −3.85410 | − | 2.80017i | −0.123812 | − | 0.0899544i | ||||
\(970\) | −1.48278 | − | 4.56352i | −0.0476092 | − | 0.146526i | ||||
\(971\) | 27.0344 | − | 19.6417i | 0.867577 | − | 0.630331i | −0.0623590 | − | 0.998054i | \(-0.519862\pi\) |
0.929936 | + | 0.367723i | \(0.119862\pi\) | |||||||
\(972\) | 0.809017 | − | 0.587785i | 0.0259492 | − | 0.0188532i | ||||
\(973\) | 31.7082 | + | 97.5878i | 1.01652 | + | 3.12852i | ||||
\(974\) | 9.70820 | 0.311071 | ||||||||
\(975\) | −22.7254 | + | 16.5110i | −0.727796 | + | 0.528775i | ||||
\(976\) | −1.61803 | −0.0517920 | ||||||||
\(977\) | −1.00658 | − | 3.09793i | −0.0322033 | − | 0.0991115i | 0.933663 | − | 0.358153i | \(-0.116593\pi\) |
−0.965866 | + | 0.259041i | \(0.916593\pi\) | |||||||
\(978\) | 12.0902 | − | 8.78402i | 0.386601 | − | 0.280882i | ||||
\(979\) | 5.38197 | − | 3.91023i | 0.172008 | − | 0.124971i | ||||
\(980\) | 29.0689 | 0.928571 | ||||||||
\(981\) | 6.39919 | + | 4.64928i | 0.204310 | + | 0.148440i | ||||
\(982\) | 5.88854 | 0.187911 | ||||||||
\(983\) | −6.70820 | − | 4.87380i | −0.213958 | − | 0.155450i | 0.475644 | − | 0.879638i | \(-0.342215\pi\) |
−0.689603 | + | 0.724188i | \(0.742215\pi\) | |||||||
\(984\) | 3.35410 | − | 10.3229i | 0.106925 | − | 0.329081i | ||||
\(985\) | −17.0344 | −0.542762 | ||||||||
\(986\) | 7.88197 | + | 24.2582i | 0.251013 | + | 0.772538i | ||||
\(987\) | 1.05573 | − | 3.24920i | 0.0336042 | − | 0.103423i | ||||
\(988\) | −2.14590 | + | 6.60440i | −0.0682701 | + | 0.210114i | ||||
\(989\) | 10.6525 | + | 32.7849i | 0.338729 | + | 1.04250i | ||||
\(990\) | 0.854102 | − | 2.62866i | 0.0271451 | − | 0.0835442i | ||||
\(991\) | 11.4721 | − | 35.3076i | 0.364424 | − | 1.12158i | −0.585916 | − | 0.810372i | \(-0.699265\pi\) |
0.950341 | − | 0.311211i | \(-0.100735\pi\) | |||||||
\(992\) | −11.1803 | − | 8.12299i | −0.354976 | − | 0.257905i | ||||
\(993\) | −6.94427 | −0.220370 | ||||||||
\(994\) | −18.9443 | − | 13.7638i | −0.600876 | − | 0.436562i | ||||
\(995\) | 22.8885 | + | 16.6295i | 0.725616 | + | 0.527191i | ||||
\(996\) | 10.0902 | − | 7.33094i | 0.319719 | − | 0.232290i | ||||
\(997\) | 14.0902 | − | 10.2371i | 0.446240 | − | 0.324212i | −0.341869 | − | 0.939747i | \(-0.611060\pi\) |
0.788110 | + | 0.615535i | \(0.211060\pi\) | |||||||
\(998\) | −1.85410 | − | 5.70634i | −0.0586906 | − | 0.180631i | ||||
\(999\) | −3.09017 | −0.0977687 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 75.2.g.a.31.1 | ✓ | 4 | |
3.2 | odd | 2 | 225.2.h.a.181.1 | 4 | |||
5.2 | odd | 4 | 375.2.i.a.349.1 | 8 | |||
5.3 | odd | 4 | 375.2.i.a.349.2 | 8 | |||
5.4 | even | 2 | 375.2.g.a.151.1 | 4 | |||
25.2 | odd | 20 | 1875.2.b.b.1249.3 | 4 | |||
25.3 | odd | 20 | 375.2.i.a.274.1 | 8 | |||
25.4 | even | 10 | 375.2.g.a.226.1 | 4 | |||
25.11 | even | 5 | 1875.2.a.d.1.1 | 2 | |||
25.14 | even | 10 | 1875.2.a.a.1.2 | 2 | |||
25.21 | even | 5 | inner | 75.2.g.a.46.1 | yes | 4 | |
25.22 | odd | 20 | 375.2.i.a.274.2 | 8 | |||
25.23 | odd | 20 | 1875.2.b.b.1249.2 | 4 | |||
75.11 | odd | 10 | 5625.2.a.a.1.1 | 2 | |||
75.14 | odd | 10 | 5625.2.a.h.1.2 | 2 | |||
75.71 | odd | 10 | 225.2.h.a.46.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.a.31.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
75.2.g.a.46.1 | yes | 4 | 25.21 | even | 5 | inner | |
225.2.h.a.46.1 | 4 | 75.71 | odd | 10 | |||
225.2.h.a.181.1 | 4 | 3.2 | odd | 2 | |||
375.2.g.a.151.1 | 4 | 5.4 | even | 2 | |||
375.2.g.a.226.1 | 4 | 25.4 | even | 10 | |||
375.2.i.a.274.1 | 8 | 25.3 | odd | 20 | |||
375.2.i.a.274.2 | 8 | 25.22 | odd | 20 | |||
375.2.i.a.349.1 | 8 | 5.2 | odd | 4 | |||
375.2.i.a.349.2 | 8 | 5.3 | odd | 4 | |||
1875.2.a.a.1.2 | 2 | 25.14 | even | 10 | |||
1875.2.a.d.1.1 | 2 | 25.11 | even | 5 | |||
1875.2.b.b.1249.2 | 4 | 25.23 | odd | 20 | |||
1875.2.b.b.1249.3 | 4 | 25.2 | odd | 20 | |||
5625.2.a.a.1.1 | 2 | 75.11 | odd | 10 | |||
5625.2.a.h.1.2 | 2 | 75.14 | odd | 10 |